簡單復(fù)合導(dǎo)數(shù)題目及答案一、單項(xiàng)選擇題1.函數(shù)\(y=\frac{1}{x}\)的導(dǎo)數(shù)是（）。A.\(y'=-\frac{1}{x^2}\)B.\(y'=\frac{1}{x^2}\)C.\(y'=-\frac{1}{x^3}\)D.\(y'=-\frac{1}{x^4}\)答案：A2.函數(shù)\(y=x^3\)的導(dǎo)數(shù)是（）。A.\(y'=3x^2\)B.\(y'=3x\)C.\(y'=3x^3\)D.\(y'=9x^2\)答案：A3.函數(shù)\(y=\sin(x)\)的導(dǎo)數(shù)是（）。A.\(y'=\cos(x)\)B.\(y'=\sin(x)\)C.\(y'=-\sin(x)\)D.\(y'=-\cos(x)\)答案：A4.函數(shù)\(y=e^x\)的導(dǎo)數(shù)是（）。A.\(y'=e^x\)B.\(y'=-e^x\)C.\(y'=e^{-x}\)D.\(y'=-e^{-x}\)答案：A5.函數(shù)\(y=\ln(x)\)的導(dǎo)數(shù)是（）。A.\(y'=\frac{1}{x}\)B.\(y'=\frac{1}{x^2}\)C.\(y'=x\)D.\(y'=\ln(x)\)答案：A二、多項(xiàng)選擇題1.函數(shù)\(y=x^2-3x+2\)的導(dǎo)數(shù)是（）。A.\(y'=2x-3\)B.\(y'=2x+3\)C.\(y'=-2x+3\)D.\(y'=-2x-3\)答案：A2.函數(shù)\(y=\sqrt{x}\)的導(dǎo)數(shù)是（）。A.\(y'=\frac{1}{2\sqrt{x}}\)B.\(y'=\frac{1}{\sqrt{x}}\)C.\(y'=\frac{1}{x}\)D.\(y'=\frac{1}{2x}\)答案：A3.函數(shù)\(y=\tan(x)\)的導(dǎo)數(shù)是（）。A.\(y'=\sec^2(x)\)B.\(y'=\tan^2(x)\)C.\(y'=\sec(x)\)D.\(y'=\csc^2(x)\)答案：A4.函數(shù)\(y=\arcsin(x)\)的導(dǎo)數(shù)是（）。A.\(y'=\frac{1}{\sqrt{1-x^2}}\)B.\(y'=\frac{1}{\sqrt{1+x^2}}\)C.\(y'=\frac{1}{x}\)D.\(y'=\frac{1}{1-x^2}\)答案：A5.函數(shù)\(y=\arctan(x)\)的導(dǎo)數(shù)是（）。A.\(y'=\frac{1}{1+x^2}\)B.\(y'=\frac{1}{1-x^2}\)C.\(y'=\frac{1}{x}\)D.\(y'=\frac{1}{x^2}\)答案：A三、填空題1.函數(shù)\(y=x^4-4x^3+6x^2-4x+1\)的導(dǎo)數(shù)是\(y'=______\)。答案：\(4x^3-12x^2+12x-4\)2.函數(shù)\(y=\cos(x)\)的導(dǎo)數(shù)是\(y'=______\)。答案：\(-\sin(x)\)3.函數(shù)\(y=\frac{1}{x^2+1}\)的導(dǎo)數(shù)是\(y'=______\)。答案：\(-\frac{2x}{(x^2+1)^2}\)4.函數(shù)\(y=\ln(x^2)\)的導(dǎo)數(shù)是\(y'=______\)。答案：\(\frac{2x}{x^2}\)5.函數(shù)\(y=e^{2x}\)的導(dǎo)數(shù)是\(y'=______\)。答案：\(2e^{2x}\)四、計算題1.求函數(shù)\(y=x^2\ln(x)\)的導(dǎo)數(shù)。答案：\(y'=2x\ln(x)+x\)2.求函數(shù)\(y=e^x\sin(x)\)的導(dǎo)數(shù)。答案：\(y'=e^x\sin(x)+e^x\cos(x)\)3.求函數(shù)\(y=\ln(x)\cos(x)\)的導(dǎo)數(shù)。答案：\(y'=\frac{\cos(x)}{x}-\ln(x)\sin(x)\)4.求函數(shù)\(y=\sqrt{x}\ln(x)\)的導(dǎo)數(shù)。答案：\(y'=\frac{\ln(x)}{2\sqrt{x}}+\