導(dǎo)數(shù)考試題型及答案解析

單項(xiàng)選擇題（每題2分，共10題）1.函數(shù)\(y=x^2\)在\(x=1\)處的導(dǎo)數(shù)是（）A.1B.2C.3D.42.若\(f(x)=e^x\)，則\(f^\prime(0)\)等于（）A.0B.1C.2D.33.函數(shù)\(y=\sinx\)的導(dǎo)數(shù)是（）A.\(\cosx\)B.\(-\cosx\)C.\(\sinx\)D.\(-\sinx\)4.曲線\(y=x^3\)在點(diǎn)\((1,1)\)處的切線方程為（）A.\(y=3x-2\)B.\(y=3x+2\)C.\(y=-3x-2\)D.\(y=-3x+2\)5.函數(shù)\(f(x)=\lnx\)的導(dǎo)數(shù)為（）A.\(\frac{1}{x}\)B.\(-\frac{1}{x}\)C.\(x\)D.\(-x\)6.已知\(y=2x^3\)，則\(y^\prime\)等于（）A.\(6x^2\)B.\(6x\)C.\(2x^2\)D.\(2x\)7.函數(shù)\(y=\cos2x\)的導(dǎo)數(shù)是（）A.\(-2\sin2x\)B.\(2\sin2x\)C.\(-\sin2x\)D.\(\sin2x\)8.曲線\(y=e^x\)在點(diǎn)\((0,1)\)處的切線斜率為（）A.0B.1C.2D.39.函數(shù)\(y=x^4\)的導(dǎo)數(shù)為（）A.\(4x^3\)B.\(4x\)C.\(x^3\)D.\(x\)10.若\(y=\frac{1}{x^2}\)，則\(y^\prime\)等于（）A.\(-\frac{2}{x^3}\)B.\(\frac{2}{x^3}\)C.\(-\frac{1}{x^3}\)D.\(\frac{1}{x^3}\)答案：1.B2.B3.A4.A5.A6.A7.A8.B9.A10.A多項(xiàng)選擇題（每題2分，共10題）1.下列求導(dǎo)正確的是（）A.\((x^2)^\prime=2x\)B.\((\sinx)^\prime=\cosx\)C.\((\lnx)^\prime=\frac{1}{x}\)D.\((e^x)^\prime=e^x\)2.函數(shù)\(y=x^3+x\)的導(dǎo)數(shù)是（）A.\(3x^2+1\)B.\(x^3+1\)C.\(3x^2\)D.\(x^3\)3.曲線\(y=x^2\)在點(diǎn)\((2,4)\)處的切線相關(guān)正確的是（）A.切線斜率為4B.切線方程為\(y=4x-4\)C.切線過點(diǎn)\((2,4)\)D.切線斜率為24.下列函數(shù)導(dǎo)數(shù)正確的是（）A.\(y=2x\)導(dǎo)數(shù)為2B.\(y=\cos3x\)導(dǎo)數(shù)為\(-3\sin3x\)C.\(y=\sqrt{x}\)導(dǎo)數(shù)為\(\frac{1}{2\sqrt{x}}\)D.\(y=x^0\)導(dǎo)數(shù)為05.函數(shù)\(f(x)=x^2-2x\)的導(dǎo)數(shù)\(f^\prime(x)\)為（）A.\(2x-2\)B.\(2x\)C.\(x-2\)D.\(2x-1\)6.曲線\(y=\sinx\)在點(diǎn)\((\frac{\pi}{2},1)\)處的情況正確的是（）A.切線斜率為0B.切線方程為\(y=1\)C.切線過點(diǎn)\((\frac{\pi}{2},1)\)D.切線斜率為17.下列求導(dǎo)運(yùn)算正確的有（）A.\((3^x)^\prime=3^x\ln3\)B.\((\log_3x)^\prime=\frac{1}{x\ln3}\)C.\((\frac{1}{x})^\prime=-\frac{1}{x^2}\)D.\((x^3)^\prime=3x^2\)8.函數(shù)\(y=2\cosx+3\sinx\)的導(dǎo)數(shù)是（）A.\(-2\sinx+3\cosx\)B.\(2\sinx+3\cosx\)C.\(-2\sinx-3\cosx\)D.\(2\sinx-3\cosx\)9.曲線\(y=x^3-3x\)在點(diǎn)\((1,-2)\)處的切線相關(guān)正確的是（）A.切線斜率為0B.切線方程為\(y=-2\)C.切線過點(diǎn)\((1,-2)\)D.切線斜率為110.函數(shù)\(y=\frac{1}{x^3}\)的導(dǎo)數(shù)為（）A.\(-\frac{3}{x^4}\)B.\(\frac{3}{x^4}\)C.\(-3x^4\)D.\(3x^4\)答案：1.ABCD2.A3.ABC4.ABCD5.A6.BC7.ABCD8.A9.BC10.A判斷題（每題2分，共10題）1.函數(shù)\(y=x\)的導(dǎo)數(shù)是\(1\)。（）2.\(y=\sin2x\)的導(dǎo)數(shù)是\(\cos2x\)。（）3.曲線\(y=x^3\)在任意點(diǎn)處切線斜率都不為負(fù)。（）4.函數(shù)\(f(x)=e^{-x}\)的導(dǎo)數(shù)是\(e^{-x}\)。（）5.\(y=\ln(2x)\)的導(dǎo)數(shù)是\(\frac{1}{2x}\)。（）6.函數(shù)\(y=x^2+1\)在\(x=0\)處導(dǎo)數(shù)為0。（）7.曲線\(y=\cosx\)在\(x=0\)處切線斜率為1。（）8.函數(shù)\(y=\frac{1}{\sqrt{x}}\)的導(dǎo)數(shù)是\(-\frac{1}{2x\sqrt{x}}\)。（）9.\(y=2^x\)的導(dǎo)數(shù)是\(2^x\ln2\)。（）10.曲線\(y=x^4\)在\((1,1)\)處切線方程為\(y=4x-3\)。（）答案：1.√2.×3.√4.×5.×6.×7.×8.√9.√10.×簡答題（總4題，每題5分）1.求\(y=x^3+2x^2-3x\)的導(dǎo)數(shù)。答案：\(y^\prime=3x^2+4x-3\)。2.已知曲線\(y=x^2\)，求在點(diǎn)\((3,9)\)處的切線方程。答案：先求斜率\(k=2\times3=6\)，切線方程為\(y-9=6(x-3)\)，即\(y=6x-9\)。3.求\(y=\sin3x\)的導(dǎo)數(shù)。答案：\(y^\prime=3\cos3x\)。4.函數(shù)\(y=\ln(x+1)\)的導(dǎo)數(shù)是多少？答案：\(y^\prime=\frac{1}{x+1}\)。討論題（總4題，每