مدیر ارشد سایت

# ماراتون مشتق

این سوالات با تلاش جناب تقی خواجه در وبلاگ شخصی ایشان با نام «آموزش ریاضی دبیرستان» منتشر شده است.

$\large&space;\begin{array}{l}&space;1)\,\,y&space;=&space;{x^5}&space;-&space;4{x^2}&space;+&space;2x&space;-&space;3\\\\&space;2)\,\,y&space;=&space;\frac{1}{4}&space;-&space;\frac{1}{3}x&space;+&space;{x^2}&space;-&space;\frac{{{x^4}}}{2}\\\\&space;3)\,\,y&space;=&space;a{x^2}&space;+&space;bx&space;+&space;c&space;\end{array}$

$\large&space;\begin{array}{l}&space;4)\,\,y&space;=&space;\frac{{&space;-&space;5{x^2}}}{a}\\\\&space;5)\,\,y&space;=&space;a{t^m}&space;+&space;b{t^{m&space;+&space;n}}\\\\&space;6)\,\,y&space;=&space;\frac{{a{x^2}&space;+&space;b}}{{\sqrt&space;{{a^2}&space;+&space;{b^2}}&space;}}\\\\&space;7)\,\,y&space;=&space;\frac{\pi&space;}{x}&space;+&space;\ln&space;2&space;\end{array}$

$\large&space;\begin{array}{l}&space;8)\,\,y&space;=&space;3{x^{\frac{2}{3}}}&space;-&space;2{x^{\frac{5}{2}}}&space;+&space;{x^{&space;-&space;2}}\\\\&space;9)\,\,y&space;=&space;{x^3}\sqrt[3]{{{x^2}}}\\\\&space;10)\,\,y&space;=&space;\frac{a}{{\sqrt[3]{{{x^2}}}}}&space;-&space;\frac{b}{{x\sqrt[3]{x}}}\\\\&space;11)\,\,y&space;=&space;\frac{{a&space;+&space;bx}}{{c&space;+&space;dx}}\\\\&space;12)\,\,y&space;=&space;\frac{{2x&space;+&space;3}}{{{x^2}&space;-&space;5x&space;+&space;5}}&space;\end{array}$

$\large&space;\begin{array}{l}&space;13)\,\,y&space;=&space;\frac{2}{{2x&space;-&space;1}}&space;-&space;\frac{1}{x}\\\\&space;14)\,\,y&space;=&space;\frac{{1&space;+&space;\sqrt&space;x&space;}}{{1&space;-&space;\sqrt&space;x&space;}}\\\\&space;15)\,y&space;=&space;5\sin&space;x&space;+&space;3\cos&space;x\\\\&space;16)\,\,y&space;=&space;\tan&space;x&space;-&space;\cot&space;x&space;\end{array}$

$\large&space;\begin{array}{l}&space;17)\,\,y&space;=&space;\frac{{\sin&space;x&space;+&space;\cos&space;x}}{{\sin&space;x&space;-&space;\cos&space;x}}\\\\&space;18)\,\,y&space;=&space;2t\sin&space;t&space;-&space;\left(&space;{{t^2}&space;-&space;2}&space;\right)\cos&space;t\\\\&space;19)\,\,y&space;=&space;\arctan&space;x&space;+&space;arc\cot&space;x\\\\&space;20)\,\,y&space;=&space;x\cot&space;x&space;\end{array}$

$\large&space;\begin{array}{l}&space;21)\,\,y&space;=&space;x\arcsin&space;x\\\\&space;22)\,\,y&space;=&space;\frac{{\left(&space;{1&space;+&space;{x^2}}&space;\right)\arctan&space;x&space;-&space;x}}{2}\\\\&space;23)\,\,y&space;=&space;{x^7}{e^x}\\\\&space;24)\,\,y&space;=&space;\left(&space;{x&space;-&space;1}&space;\right){e^x}&space;\end{array}$

$\large&space;\begin{array}{l}&space;25)\,\,y&space;=&space;\frac{{{e^x}}}{{{x^2}}}\\\\&space;26)\,\,y&space;=&space;{e^x}\cos&space;x\\\\&space;27)\,y&space;=&space;\left(&space;{{x^2}&space;-&space;2x&space;+&space;2}&space;\right){e^x}\\\\&space;28)\,\,y&space;=&space;{e^x}\arcsin&space;x&space;\end{array}$

$\large&space;\begin{array}{l}&space;29)\,\,y&space;=&space;\frac{{{x^2}}}{{\ln&space;x}}\\\\&space;30)\,\,y&space;=&space;{x^2}\ln&space;x&space;-&space;\frac{{{x^2}}}{3}\\\\&space;31)\,\,y&space;=&space;\frac{1}{x}&space;+&space;2\ln&space;x&space;-&space;\frac{{\ln&space;x}}{x}\\\\&space;32)\,\,y&space;=&space;\ln&space;x\log&space;x&space;-&space;\ln&space;a\log&space;_a^x&space;\end{array}$

$\large&space;\begin{array}{l}&space;33)\,\,y&space;=&space;{\left(&space;{1&space;+&space;3x&space;-&space;5{x^2}}&space;\right)^{30}}\\\\&space;34)\,\,y&space;=&space;{\left(&space;{\frac{{ax&space;+&space;b}}{c}}&space;\right)^2}\\\\&space;35)\,\,y&space;=&space;{\left(&space;{2a&space;+&space;3bx}&space;\right)^2}\\\\&space;36)\,\,y&space;=&space;{\left(&space;{3&space;+&space;2{x^2}}&space;\right)^4}&space;\end{array}$

$\large&space;\begin{array}{l}&space;37)\,\,y&space;=&space;\frac{3}{{56{{\left(&space;{2x&space;-&space;1}&space;\right)}^7}}}&space;-&space;\frac{1}{{24{{\left(&space;{2x&space;-&space;1}&space;\right)}^6}}}&space;-&space;\frac{1}{{40{{\left(&space;{2x&space;-&space;1}&space;\right)}^5}}}\\\\&space;38)\,\,y&space;=&space;\sqrt&space;{1&space;-&space;{x^2}}&space;\end{array}$

$\large&space;\begin{array}{l}&space;39)\,\,y&space;=&space;\sqrt[3]{{a&space;+&space;b{x^3}}}\\\\&space;40)\,\,y&space;=&space;{\left(&space;{{a^{\frac{2}{3}}}&space;-&space;{x^{\frac{2}{3}}}}&space;\right)^{\frac{1}{2}}}&space;\end{array}$

$\large&space;\begin{array}{l}&space;41)\,\,y&space;=&space;{\left(&space;{3&space;-&space;2\sin&space;x}&space;\right)^3}\\\\&space;42)\,\,y&space;=&space;\tan&space;x&space;-&space;\frac{1}{3}{\tan&space;^3}x&space;+&space;\frac{1}{5}{\tan&space;^5}x\\\\&space;42)\,\,y&space;=&space;\sqrt&space;{\cot&space;x}&space;-&space;\sqrt&space;{\cot&space;a}&space;\\\\&space;43)\,\,y&space;=&space;2x&space;+&space;5{\cos&space;^2}x&space;\end{array}$

$\large&space;\begin{array}{l}&space;44)\,\,y&space;=&space;\frac{1}{{{{\sin&space;}^2}x}}&space;+&space;\frac{1}{{{{\cos&space;}^2}x}}\\\\&space;45)\,\,y&space;=&space;-&space;\frac{1}{{6{{\left(&space;{1&space;-&space;3\cos&space;x}&space;\right)}^2}}}\\\\&space;46)\,\,y&space;=&space;\sqrt&space;{1&space;+&space;\arcsin&space;x}&space;\\\\&space;47)\,\,y&space;=&space;\sqrt&space;{\arctan&space;x}&space;-&space;{\left(&space;{\arcsin&space;x}&space;\right)^2}&space;\end{array}$

$\large&space;\begin{array}{l}&space;48)\,\,y&space;=&space;\frac{1}{{\arctan&space;x}}\\\\&space;49)\,\,y&space;=&space;\sqrt&space;{x{e^x}&space;+&space;x}&space;\\\\&space;50)\,\,y&space;=&space;\sqrt[3]{{2{e^x}&space;-&space;{2^x}&space;+&space;1}}&space;+&space;{\ln&space;^5}x\\\\&space;51)\,\,y&space;=&space;\sin&space;3x&space;+&space;\cos&space;\frac{x}{5}&space;+&space;\tan&space;\sqrt&space;x&space;\end{array}$

$\large&space;\begin{array}{l}&space;52)\,\,y&space;=&space;\frac{1}{{3{{\cos&space;}^2}x}}&space;-&space;\frac{1}{{\cos&space;x}}\\\\&space;53)\,\,y&space;=&space;\sqrt&space;{\frac{{3\sin&space;x&space;-&space;2\cos&space;x}}{5}}&space;\\\\&space;54)\,\,y&space;=&space;\sqrt[3]{{{{\sin&space;}^2}x}}&space;+&space;\frac{1}{{{{\cos&space;}^2}x}}\\\\&space;55)\,\,y&space;=&space;\sin&space;\left(&space;{{x^2}&space;-&space;5x&space;+&space;1}&space;\right)&space;+&space;\tan&space;\frac{a}{x}&space;\end{array}$

$\large&space;\begin{array}{l}&space;56)\,\,y&space;=&space;\cos&space;\left(&space;{\alpha&space;x&space;+&space;\beta&space;}&space;\right)\\\\&space;57)\,\,y&space;=&space;\sin&space;x\sin&space;\left(&space;{x&space;+&space;\alpha&space;}&space;\right)\\\\&space;58)\,\,y&space;=&space;\frac{{1&space;+&space;\cos&space;2x}}{{1&space;-&space;\cos&space;2x}}\\\\&space;59)\,\,y&space;=&space;a\cot&space;\frac{x}{a}\\\\&space;60)\,\,y&space;=&space;-&space;\frac{1}{{20}}\cos&space;\left(&space;{5{x^2}}&space;\right)&space;-&space;\frac{1}{4}\cos&space;\left(&space;{{x^2}}&space;\right)&space;\end{array}$

$\large&space;\begin{array}{l}&space;61)\,\,y&space;=&space;\arcsin&space;2x\\\\&space;62)\,\,y&space;=&space;\arcsin&space;\frac{1}{{{x^2}}}\\\\&space;63)\,\,y&space;=&space;\arccos&space;\sqrt&space;x&space;\\\\&space;64)\,\,y&space;=&space;\arctan&space;\frac{1}{x}\\\\&space;65)\,\,y&space;=&space;arc\cot&space;\frac{{1&space;+&space;x}}{{1&space;-&space;x}}&space;\end{array}$

$\large&space;\begin{array}{l}&space;66)\,\,y&space;=&space;5{e^{&space;-&space;{x^2}}}\\\\&space;67)\,\,y&space;=&space;\frac{1}{{{5^{{x^2}}}}}\\\\&space;68)\,\,y&space;=&space;{x^2}\left(&space;{{{10}^{2x}}}&space;\right)\\\\&space;69)\,\,y&space;=&space;x\sin&space;{2^x}\\\\&space;70)\,\,y&space;=&space;\ln&space;\left(&space;{{e^x}&space;+&space;5\sin&space;x&space;-&space;4\arcsin&space;x}&space;\right)&space;\end{array}$

$\large&space;\begin{array}{l}&space;71)\,\,y&space;=&space;\arctan&space;\left(&space;{\ln&space;x}&space;\right)&space;+&space;\ln&space;\left(&space;{\arctan&space;x}&space;\right)\\\\&space;72)\,\,y&space;=&space;\sqrt&space;{\ln&space;x&space;+&space;1}&space;+&space;\ln&space;\left(&space;{\sqrt&space;x&space;+&space;1}&space;\right)\\\\&space;73)\,\,y&space;=&space;\arccos&space;{e^x}\\\\&space;74)\,\,y&space;=&space;\ln&space;\left(&space;{2x&space;+&space;7}&space;\right)\\\\&space;75)\,\,y&space;=&space;\log&space;\left(&space;{\sin&space;x}&space;\right)&space;\end{array}$

$\large&space;\begin{array}{l}&space;76)\,\,y&space;=&space;\ln&space;\left(&space;{1&space;-&space;{x^2}}&space;\right)\\\\&space;77)\,\,y&space;=&space;{\ln&space;^2}x&space;-&space;\ln&space;\left(&space;{\ln&space;x}&space;\right)\\\\&space;78)\,\,y&space;=&space;{\sin&space;^3}5x{\cos&space;^2}\frac{x}{3}\\\\&space;79)\,\,y&space;=&space;-&space;\frac{{11}}{{2{{\left(&space;{x&space;-&space;2}&space;\right)}^2}}}&space;-&space;\frac{4}{{x&space;-&space;2}}&space;\end{array}$

$\large&space;\begin{array}{l}&space;80)\,\,y&space;=&space;-&space;\frac{{15}}{{4{{\left(&space;{x&space;-&space;3}&space;\right)}^4}}}&space;-&space;\frac{{10}}{{3{{\left(&space;{x&space;-&space;3}&space;\right)}^3}}}&space;-&space;\frac{1}{{2{{\left(&space;{x&space;-&space;3}&space;\right)}^2}}}\\\\&space;81)\,\,y&space;=&space;\frac{{{x^2}}}{{8{{\left(&space;{1&space;-&space;{x^2}}&space;\right)}^4}}}\\\\&space;82)\,\,y&space;=&space;\frac{{\sqrt&space;{2{x^2}&space;-&space;2x&space;+&space;1}&space;}}{x}\\\\&space;83)\,\,y&space;=&space;\frac{x}{{{a^2}\sqrt&space;{{a^2}&space;+&space;{x^2}}&space;}}&space;\end{array}$

$\large&space;\begin{array}{l}&space;84)\,\,y&space;=&space;\frac{{{x^2}}}{{3\sqrt&space;{{{\left(&space;{1&space;+&space;{x^2}}&space;\right)}^3}}&space;}}\\\\&space;85)\,\,y&space;=&space;\frac{3}{2}\sqrt[3]{{{x^2}}}&space;+&space;\frac{{18}}{7}x\sqrt[6]{x}&space;+&space;\frac{9}{5}x\sqrt[3]{{{x^2}}}&space;+&space;\frac{6}{{13}}{x^2}\sqrt[6]{x}\\\\&space;86)\,\,y&space;=&space;\frac{1}{8}\sqrt[3]{{{{\left(&space;{1&space;+&space;{x^2}}&space;\right)}^3}}}&space;-&space;\frac{1}{5}\sqrt[3]{{{{\left(&space;{1&space;+&space;{x^2}}&space;\right)}^5}}}&space;\end{array}$

$\large&space;\begin{array}{l}&space;87)\,\,y&space;=&space;\frac{4}{3}\sqrt&space;{\frac{{x&space;-&space;1}}{{x&space;+&space;2}}}&space;\\\\&space;88)\,\,y&space;=&space;{x^4}{\left(&space;{a&space;-&space;2{x^3}}&space;\right)^2}\\\\&space;89)\,\,y&space;=&space;{\left(&space;{\frac{{a&space;+&space;b{x^n}}}{{a&space;-&space;b{x^n}}}}&space;\right)^m}\\\\&space;90)\,\,y&space;=&space;\frac{9}{{5{{\left(&space;{x&space;+&space;2}&space;\right)}^5}}}&space;-&space;\frac{3}{{{{\left(&space;{x&space;+&space;2}&space;\right)}^4}}}&space;+&space;\frac{2}{{{{\left(&space;{x&space;+&space;2}&space;\right)}^3}}}&space;-&space;\frac{1}{{2{{\left(&space;{x&space;+&space;2}&space;\right)}^2}}}&space;\end{array}$

$\large&space;\begin{array}{l}&space;91)\,\,y&space;=&space;\left(&space;{a&space;+&space;x}&space;\right)\sqrt&space;{a&space;-&space;x}&space;\\\\&space;92)\,\,y&space;=&space;\sqrt&space;{\left(&space;{x&space;+&space;a}&space;\right)\left(&space;{x&space;+&space;b}&space;\right)\left(&space;{x&space;+&space;c}&space;\right)}&space;\\\\&space;93)\,\,y&space;=&space;\sqrt[3]{{x&space;+&space;\sqrt&space;x&space;}}\\\\&space;94)\,\,y&space;=&space;\left(&space;{2x&space;+&space;1}&space;\right)\left(&space;{3x&space;+&space;2}&space;\right)\sqrt[3]{{3x&space;+&space;2}}\\\\&space;95)\,\,y&space;=&space;\frac{1}{{\sqrt&space;{2ax&space;-&space;{x^2}}&space;}}&space;\end{array}$

$\large&space;\begin{array}{l}&space;96)\,\,y&space;=&space;\ln&space;\left(&space;{\sqrt&space;{1&space;+&space;{e^x}}&space;-&space;1}&space;\right)&space;-&space;\ln&space;\left(&space;{\sqrt&space;{1&space;+&space;{e^x}}&space;+&space;1}&space;\right)\\\\&space;97)\,\,y&space;=&space;\frac{1}{{15}}{\cos&space;^2}x\left(&space;{3{{\cos&space;}^2}x&space;-&space;5}&space;\right)\\\\&space;98)\,\,y&space;=&space;\frac{{\left(&space;{{{\tan&space;}^2}x&space;-&space;1}&space;\right)\left(&space;{{{\tan&space;}^4}x&space;+&space;10{{\tan&space;}^2}x&space;+&space;1}&space;\right)}}{{3{{\tan&space;}^3}x}}\\\\&space;99)\,\,y&space;=&space;{\tan&space;^5}5x\\\\&space;100)\,\,y&space;=&space;\frac{1}{2}\sin&space;\left(&space;{{x^2}}&space;\right)&space;\end{array}$

$\large&space;\begin{array}{l}&space;101)\,\,y&space;=&space;{\sin&space;^2}\left(&space;{{x^3}}&space;\right)\\\\&space;102)\,\,y&space;=&space;3\sin&space;x{\cos&space;^2}x&space;+&space;{\sin&space;^2}x\\\\&space;103)\,\,y&space;=&space;\frac{1}{3}{\tan&space;^3}x&space;-&space;\tan&space;x&space;+&space;x\\\\&space;104)\,\,y&space;=&space;-&space;\frac{{\cos&space;x}}{{3{{\sin&space;}^3}x}}&space;+&space;\frac{4}{3}\cot&space;x&space;\end{array}$

$\large&space;\begin{array}{l}&space;105)\,\,y&space;=&space;\sqrt&space;{\alpha&space;{{\sin&space;}^2}x&space;+&space;\beta&space;{{\cos&space;}^2}x}&space;\\\\&space;106)\,\,y&space;=&space;\arcsin&space;{x^2}&space;+&space;\arccos&space;{x^2}\\\\&space;107)\,\,y&space;=&space;\arcsin&space;\frac{{{x^2}&space;-&space;1}}{{{x^2}}}\\\\&space;108)\,\,y&space;=&space;\arcsin&space;\frac{x}{{\sqrt&space;{1&space;+&space;{x^2}}&space;}}&space;\end{array}$

$\large&space;\begin{array}{l}&space;109)\,\,y&space;=&space;\frac{{\arccos&space;x}}{{\sqrt&space;{1&space;-&space;{x^2}}&space;}}\\\\&space;110)\,\,y&space;=&space;\frac{1}{{\sqrt&space;b&space;}}\arcsin&space;\left(&space;{x\sqrt&space;{\frac{b}{a}}&space;}&space;\right)\\\\&space;111)\,\,y&space;=&space;\sqrt&space;{{a^2}&space;-&space;{x^2}}&space;+&space;\arcsin&space;\frac{x}{a}\\\\&space;112)\,\,y&space;=&space;x\sqrt&space;{{a^2}&space;-&space;{x^2}}&space;+&space;\arcsin&space;\frac{x}{a}&space;\end{array}$

$\large&space;\begin{array}{l}&space;113)\,\,y&space;=&space;x\sqrt&space;{{a^2}&space;-&space;{x^2}}&space;+&space;{a^2}\arcsin&space;\frac{x}{a}\\\\&space;114)\,\,y&space;=&space;\arcsin&space;\left(&space;{1&space;-&space;x}&space;\right)&space;+&space;\sqrt&space;{2x&space;-&space;{x^2}}&space;\\\\&space;115)\,\,y&space;=&space;\frac{1}{2}{\left(&space;{\arcsin&space;x}&space;\right)^2}\arccos&space;x\\\\&space;116)\,\,y&space;=&space;\left(&space;{x&space;-&space;\frac{1}{2}}&space;\right)\arcsin&space;\sqrt&space;x&space;+&space;\frac{1}{2}\sqrt&space;{x&space;-&space;{x^2}}&space;\end{array}$

$\large&space;\begin{array}{l}&space;117)\,\,y&space;=&space;\ln&space;\left(&space;{\arcsin&space;5x}&space;\right)\\\\&space;118)\,\,y&space;=&space;\arcsin&space;\left(&space;{\ln&space;x}&space;\right)\\\\&space;119)\,\,y&space;=&space;\arctan&space;\frac{{x\sin&space;a}}{{1&space;-&space;x\cos&space;a}}\\\\&space;120)\,\,y&space;=&space;\frac{2}{3}\arctan&space;\frac{{5\tan&space;\frac{x}{2}&space;+&space;4}}{3}&space;\end{array}$

$\large&space;\begin{array}{l}&space;121)\,\,y&space;=&space;3{b^2}\arctan&space;\sqrt&space;{\frac{x}{{b&space;-&space;x}}}&space;-&space;\left(&space;{3b&space;+&space;2x}&space;\right)\sqrt&space;{bx&space;-&space;{x^2}}&space;\\\\&space;122)\,\,y&space;=&space;-&space;\sqrt&space;2&space;arc\cot&space;\frac{{\tan&space;x}}{{\sqrt&space;2&space;}}&space;-&space;x\\\\&space;123)\,\,y&space;=&space;\sqrt&space;{{e^{ax}}}&space;\\\\&space;124)\,\,y&space;=&space;{e^{{{\sin&space;}^2}x}}\\\\&space;125)\,\,y&space;=&space;{\left(&space;{2m{a^{mx}}&space;+&space;b}&space;\right)^p}&space;\end{array}$

$\large&space;\begin{array}{l}&space;126)\,\,y&space;=&space;{e^{\alpha&space;x}}\cos&space;\beta&space;x\\\\&space;127)\,\,y&space;=&space;\frac{{\left(&space;{\alpha&space;\sin&space;\beta&space;x&space;-&space;\beta&space;\cos&space;\beta&space;x}&space;\right){e^{\alpha&space;x}}}}{{{\alpha&space;^2}&space;+&space;{\beta&space;^2}}}\\\\&space;128)\,\,y&space;=&space;\frac{1}{{10}}{e^{&space;-&space;x}}\left(&space;{3\sin&space;3x&space;-&space;\cos&space;3x}&space;\right)\\\\&space;129)\,\,y&space;=&space;{x^n}{a^{&space;-&space;{x^2}}}\\\\&space;130)\,\,y&space;=&space;\sqrt&space;{\cos&space;x}&space;{a^{\sqrt&space;{\cos&space;x}&space;}}&space;\end{array}$

$\large&space;\begin{array}{l}&space;131)\,\,y&space;=&space;x&space;-&space;2\sqrt&space;x&space;+&space;2\ln&space;\left(&space;{1&space;+&space;\sqrt&space;x&space;}&space;\right)\\\\&space;132)\,\,y&space;=&space;\ln&space;\left(&space;{a&space;+&space;x&space;+&space;\sqrt&space;{2ax&space;+&space;{x^2}}&space;}&space;\right)\\\\&space;133)\,\,y&space;=&space;\frac{1}{{{{\ln&space;}^2}x}}\\\\&space;134)\,\,y&space;=&space;\ln&space;\cos&space;\frac{{x&space;-&space;1}}{x}\\\\&space;135)\,\,y&space;=&space;\frac{x}{2}\sqrt&space;{{x^2}&space;-&space;{a^2}}&space;-&space;\frac{{{a^2}}}{2}\ln&space;\left(&space;{x&space;+&space;\sqrt&space;{{x^2}&space;-&space;{a^2}}&space;}&space;\right)&space;\end{array}$

$\large&space;\begin{array}{l}&space;136)\,\,y&space;=&space;\,\ln&space;\ln&space;\left(&space;{3&space;-&space;2{x^3}}&space;\right)\\\\&space;137)\,\,y&space;=&space;5{\ln&space;^3}\left(&space;{ax&space;+&space;b}&space;\right)\\\\&space;138)\,\,y&space;=&space;\ln&space;\frac{{\sqrt&space;{{x^2}&space;+&space;{a^2}}&space;+&space;x}}{{\sqrt&space;{{x^2}&space;+&space;{a^2}}&space;-&space;x}}\\\\&space;139)\,\,y&space;=&space;\frac{m}{2}\ln&space;\left(&space;{{x^2}&space;-&space;{a^2}}&space;\right)&space;+&space;\frac{n}{{2a}}\ln&space;\frac{{x&space;-&space;a}}{{x&space;+&space;a}}\\\\&space;140)\,\,y&space;=&space;x\sin&space;\left(&space;{\ln&space;x&space;-&space;\frac{\pi&space;}{4}}&space;\right)&space;\end{array}$

$\large&space;\begin{array}{l}&space;141)\,\,y&space;=&space;\frac{1}{2}\ln&space;\tan&space;\frac{x}{2}&space;-&space;\frac{1}{2}\frac{{\cos&space;x}}{{{{\sin&space;}^2}x}}\\\\&space;142)\,\,y&space;=&space;\sqrt&space;{{x^2}&space;+&space;1}&space;-&space;\ln&space;\frac{{1&space;+&space;\sqrt&space;{{x^2}&space;+&space;1}&space;}}{x}&space;\end{array}$

$\large&space;\begin{array}{l}&space;143)\,\,y&space;=&space;\frac{1}{3}\ln&space;\frac{{{x^2}&space;-&space;2x&space;+&space;1}}{{{x^2}&space;+&space;x&space;+&space;1}}\\\\&space;144)\,\,y&space;=&space;{2^{2\arcsin&space;3x}}&space;+&space;{\left(&space;{1&space;-&space;\arccos&space;3x}&space;\right)^2}\\\\&space;145)\,\,y&space;=&space;{3^{\frac{{\sin&space;ax}}{{\cos&space;bx}}}}&space;+&space;\frac{1}{3}\frac{{{{\sin&space;}^3}ax}}{{{{\cos&space;}^3}ax}}&space;\end{array}$

$\large&space;\begin{array}{l}&space;146)\,\,y&space;=&space;\frac{1}{{\sqrt&space;3&space;}}\ln&space;\frac{{\tan&space;\frac{x}{2}&space;+&space;2&space;-&space;\sqrt&space;3&space;}}{{\tan&space;\frac{x}{2}&space;+&space;2&space;+&space;\sqrt&space;3&space;}}\\\\&space;147)\,\,y&space;=&space;\arctan&space;\left(&space;{\ln&space;x}&space;\right)\\\\&space;148)\,\,y&space;=&space;\ln&space;\left(&space;{\arcsin&space;x}&space;\right)&space;+&space;\frac{1}{2}{\ln&space;^2}x&space;+&space;\arcsin&space;\left(&space;{\ln&space;x}&space;\right)\\\\&space;149)\,\,y&space;=&space;\arctan&space;\left(&space;{\ln&space;\left(&space;{\frac{1}{x}}&space;\right)}&space;\right)&space;\end{array}$

$\large&space;\begin{array}{l}&space;150)\,\,y&space;=&space;\frac{{\sqrt&space;2&space;}}{3}\arctan&space;\frac{x}{{\sqrt&space;2&space;}}&space;+&space;\frac{1}{6}\ln&space;\frac{{x&space;-&space;1}}{{x&space;+&space;1}}\\\\&space;151)\,\,y&space;=&space;\ln&space;\frac{{1&space;+&space;\sqrt&space;{\sin&space;x}&space;}}{{1&space;-&space;\sqrt&space;{\sin&space;x}&space;}}&space;+&space;2\arctan&space;\sqrt&space;{\sin&space;x}&space;\\\\&space;152)\,\,y&space;=&space;\frac{3}{4}\ln&space;\frac{{{x^2}&space;+&space;1}}{{{x^2}&space;-&space;1}}&space;+&space;\frac{1}{4}\ln&space;\frac{{x&space;-&space;1}}{{x&space;+&space;1}}&space;+&space;\frac{1}{2}\arctan&space;x\\\\&space;153)\,\,y&space;=&space;\frac{1}{2}\ln&space;\left(&space;{1&space;+&space;x}&space;\right)&space;-&space;\frac{1}{6}\ln&space;\left(&space;{{x^2}&space;-&space;x&space;+&space;1}&space;\right)&space;+&space;\frac{1}{{\sqrt&space;3&space;}}\arctan&space;\frac{{2x&space;-&space;1}}{{\sqrt&space;3&space;}}&space;\end{array}$

$\large&space;\begin{array}{l}&space;154)\,\,y&space;=&space;\frac{{x\arcsin&space;x}}{{\sqrt&space;{1&space;-&space;{x^2}}&space;}}&space;+&space;\ln&space;\sqrt&space;{1&space;-&space;{x^2}}&space;\\\\&space;155)\,\,y&space;=&space;\left|&space;x&space;\right|\\\\&space;156)\,\,y&space;=&space;x\left|&space;x&space;\right|\\\\&space;157)\,\,y&space;=&space;\sqrt[3]{{{x^2}}}\frac{{1&space;-&space;x}}{{1&space;+&space;{x^2}}}{\sin&space;^3}x{\cos&space;^2}x\\\\&space;158)\,\,y&space;=&space;{\left(&space;{\sin&space;x}&space;\right)^x}&space;\end{array}$

$\large&space;\begin{array}{l}&space;159)\,\,y&space;=&space;\left(&space;{x&space;+&space;1}&space;\right)\left(&space;{2x&space;+&space;1}&space;\right)\left(&space;{3x&space;+&space;1}&space;\right)\\\\&space;160)\,\,y&space;=&space;\frac{{{{\left(&space;{x&space;+&space;2}&space;\right)}^2}}}{{{{\left(&space;{x&space;+&space;1}&space;\right)}^3}{{\left(&space;{x&space;+&space;3}&space;\right)}^4}}}\\\\&space;161)\,\,y&space;=&space;\sqrt&space;{\frac{{x\left(&space;{x&space;-&space;1}&space;\right)}}{{x&space;-&space;2}}}&space;\end{array}$

$\large&space;\begin{array}{l}&space;162)\,\,y&space;=&space;x\,&space;\times&space;\sqrt[3]{{\frac{{{x^2}}}{{{x^2}&space;+&space;1}}}}\\\\&space;163)\,\,y&space;=&space;\frac{{{{\left(&space;{x&space;-&space;2}&space;\right)}^9}}}{{\sqrt&space;{{{\left(&space;{x&space;-&space;1}&space;\right)}^5}{{\left(&space;{x&space;-&space;3}&space;\right)}^{11}}}&space;}}\\\\&space;164)\,\,y&space;=&space;\frac{{\sqrt&space;{x&space;-&space;1}&space;}}{{\sqrt[3]{{{{\left(&space;{x&space;+&space;2}&space;\right)}^2}}}\sqrt&space;{{{\left(&space;{x&space;+&space;3}&space;\right)}^3}}&space;}}\\\\&space;165)\,\,y&space;=&space;{x^x}&space;\end{array}$

$\large&space;\begin{array}{l}&space;166)\,\,y&space;=&space;{x^{{x^2}}}\\\\&space;167)\,\,y&space;=&space;\sqrt[x]{x}\\\\&space;168)\,\,y&space;=&space;{x^{\sqrt&space;x&space;}}\\\\&space;169)\,\,y&space;=&space;{x^{{x^x}}}\\\\&space;170)\,\,y&space;=&space;{x^{\sin&space;x}}&space;\end{array}$

$\large&space;\begin{array}{l}&space;171)\,\,y&space;=&space;{\left(&space;{\cos&space;x}&space;\right)^{\sin&space;x}}\\\\&space;172)\,\,y&space;=&space;{\left(&space;{1&space;+&space;\frac{1}{x}}&space;\right)^x}\\\\&space;173)\,\,y&space;=&space;{\left(&space;{\arctan&space;x}&space;\right)^x}\\\\&space;174)\,\,2x&space;-&space;5y&space;+&space;10&space;=&space;0&space;\end{array}$

$\large&space;\begin{array}{l}&space;175)\,\,\frac{{{x^2}}}{{{a^2}}}&space;+&space;\frac{{{y^2}}}{{{b^2}}}&space;=&space;1\\\\&space;176)\,\,{x^3}&space;+&space;{y^3}&space;=&space;{a^3}&space;\end{array}$

$\large&space;\begin{array}{l}&space;177)\,\,{x^3}&space;+&space;{x^2}y&space;+&space;{y^2}&space;=&space;0\\\\&space;178)\,\,\sqrt&space;x&space;+&space;\sqrt&space;y&space;=&space;\sqrt&space;a&space;\\\\&space;179)\,\,\sqrt[3]{{{x^2}}}&space;+&space;\sqrt[3]{{{y^2}}}&space;=&space;\sqrt[3]{{{a^2}}}\\\\&space;180)\,\,{y^3}&space;=&space;\frac{{x&space;-&space;y}}{{x&space;+&space;y}}&space;\end{array}$

$\large&space;\begin{array}{l}&space;181)\,\,y&space;-&space;0/3\sin&space;y&space;=&space;x\\\\&space;182)a{\cos&space;^2}\left(&space;{x&space;+&space;y}&space;\right)&space;=&space;b\\\\&space;183)\tan&space;y&space;=&space;xy\\\\&space;184)xy&space;=&space;\arctan&space;\frac{x}{y}\\\\&space;185)\,\,\arctan&space;\left(&space;{x&space;+&space;y}&space;\right)&space;=&space;x&space;\end{array}$

$\large&space;\begin{array}{l}&space;186)\,\,{e^y}&space;=&space;x&space;+&space;y\\\\&space;187)\,\,\ln&space;x&space;+&space;{e^{&space;-&space;\frac{y}{x}}}&space;=&space;c\\\\&space;188)\,\,\ln&space;y&space;+&space;\frac{x}{y}&space;=&space;c\\\\&space;189)\,\,\arctan&space;\frac{y}{x}&space;=&space;\frac{1}{2}\ln&space;\left(&space;{{x^2}&space;+&space;{y^2}}&space;\right)&space;\end{array}$

تعداد سئوالات 190 می باشد زیرا شماره42 تکرار شده است چون اصلاح تمام شماره مشکل بود ، به همین صورت باقی ماند پوزش بنده را بپذیرید.
مطلب قبلی ریاضی یک همراه با پاسخ
مطلب بعدی مسائل حل نشده توپولوژی
چاپ
2241 رتبه بندی این مطلب:
5/0

#### مدیر ارشد سایتمدیر ارشد سایت

سایر نوشته ها توسط مدیر ارشد سایت

### نوشتن یک نظر

 نام: لطفا نام خود را وارد نمایید. ایمیل: لطفا یک آدرس ایمیل وارد نمایید لطفا یک آدرس ایمیل معتبر وارد نمایید
 نظر: لطفا یک نظر وارد نمایید