导数英文试题及答案
一、单项选择题（每题2分，共20分）
1.Thederivativeofthefunction\(y=x^3\)is()
A.\(y=3x\)B.\(y=3x^2\)C.\(y=x^2\)D.\(y=2x\)
2.If\(y=\sinx\),then\(y=()\)
A.\(\cosx\)B.\(-\cosx\)C.\(\sinx\)D.\(-\sinx\)
3.Thederivativeof\(y=e^x\)is()
A.\(y=e^x\)B.\(y=xe^{x-1}\)C.\(y=\lnx\)D.\(y=\frac{1}{x}\)
4.Given\(y=\lnx\),\(y=()\)
A.\(x\)B.\(\frac{1}{x}\)C.\(-\frac{1}{x}\)D.\(x^2\)
5.If\(y=5x^4\),then\(y=()\)
A.\(20x^3\)B.\(5x^3\)C.\(4x^3\)D.\(20x^4\)
6.Thederivativeof\(y=\cos(2x)\)is()
A.\(y=-2\sin(2x)\)B.\(y=2\sin(2x)\)C.\(y=-\sin(2x)\)D.\(y=\sin(2x)\)
7.Forthefunction\(y=\frac{1}{x^2}\),itsderivative\(y=()\)
A.\(\frac{2}{x^3}\)B.\(-\frac{2}{x^3}\)C.\(\frac{1}{x^3}\)D.\(-\frac{1}{x^3}\)
8.If\(y=x\sinx\),then\(y=()\)
A.\(\sinx+x\cosx\)B.\(\sinx-x\cosx\)C.\(x\cosx\)D.\(\sinx\)
9.Thederivativeof\(y=\tanx\)is()
A.\(y=\sec^2x\)B.\(y=-\sec^2x\)C.\(y=\csc^2x\)D.\(y=-\csc^2x\)
10.Given\(y=3^x\),\(y=()\)
A.\(x\cdot3^{x-1}\)B.\(3^x\ln3\)C.\(3^x\)D.\(3^x\lnx\)
二、多项选择题（每题2分，共20分）
1.Whichofthefollowingstatementsaboutderivativesarecorrect?()
A.Thederivativeofaconstantfunction\(y=C\)(\(C\)isaconstant)is\(y=0\)
B.\((uv)=uv+uv\)(productrule)
C.\((\frac{u}{v})=\frac{uv-uv}{v^2}\)(\(v\neq0\),quotientrule)
D.Thederivativeof\(y=x^n\)(\(n\inR\))is\(y=nx^{n-1}\)
2.Whichofthefollowingfunctionshavederivatives?()
A.\(y=|x|\)at\(x=0\)B.\(y=x^2+1\)
C.\(y=\sqrt{x}\)(\(x0\))D.\(y=\frac{1}{x-1}\)(\(x\neq1\))
3.Thederivativeofwhichofthefollowingfunctionsisrelatedtotrigonometricfunctions?()
A.\(y=\sin^2x\)B.\(y=\cos(x+\frac{\pi}{2})\)
C.\(y=\tan\frac{x}{2}\)D.\(y=\cotx\)
4.If\(y=f(x)g(x)\),and\(f(x)\)and\(g(x)\)aredifferentiablefunctions,then\(y\)canbe