Question

设f(x),g(x)可导,求下列函数的导数1）y=根号下1+f²(x)+g²（x) 2)y=e的f&

Answer 1

f(x),g(x)处处可导求下列函数的导数

1）y=f(x+e的-x次幂)

y' = f'[x+e^(-x))]*[1-e^(-x)]

2）y=f(e的x次幂）× e的g(x)次幂

y' = e^x * f'(e^x)*e^g(x) + f(e^x)*e^g(x) * g'(x)

3)y={xf(x²）}²

y' = 2xf(x^2)*[f(x^2) + x*2x * f '(x^2)]