求下列函数的导数 1)y=ln(x2+3) 2)y=excosx 3)y=√x-1/x 4)Y=x2/x-1

Question

我本科网络学员，答案详细点，谢谢

Answer 1

1)y=ln(x2+3)
y'=1/(x²+2)*(x²+3)'=2x/(x²+3)

2)y=e^xcosx
y'=e^xcosx+e^x（-sinx)
=e^x(cosx-sinx)

3) y=√x-1/x
y'=1/(2√x)+1/x²

是这样吧
y=√[(x-1)/x ]
y'=1/2*√[x/(x-1)]*[(x-1)/x]'
=1/2*√[x/(x-1)]*[x-(x-1)])/x²
=1/2*√[x/(x-1)]*1/x²
=1/(2x²)*√[x/(x-1)]

4)Y=x²/(x-1 )
y'=[2x(x-1)-x²]/(x-1)²
=（x²-2x)/(x-1)²本回答被提问者和网友采纳

Answer 2

1)y=ln(x2+3) x2是x^2的意思么？就当是这样了
y'=[1/(x^2+3)]*2x
2)y=excosx ex是e^x吧
y'=e^x*cosx-e^x*sinx=(cosx-sinx)e^x=√2cos(x+45°)e^x
3)y=√x-1/x
y'=1/2*x^(-1/2)+x^(-2)
4)Y=x2/x-1 x2是x^2的意思么？就当是这样了 x-1是分母吧？应该有括号
y=(x^2-x+x-1+1)/(x-1)=x+1+1/(x-1)

y'=1+0-(x-1)^(-2)