Question

求y=f(e^x)*e^(f(x))的导数.

Answer 1

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

[f(e^x)]'=f'(e^x)*(e^x)'=f'(e^x)*e^x

[e^(f(x))]'=e^(f(x))*[f(x)]'=e^(f(x))*f'(x)

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