导数公式:(f(x)^(g(x)))'=?如题即f(x)的g(x)次方的导数

问题描述:

导数公式:(f(x)^(g(x)))'=?
如题
即f(x)的g(x)次方的导数

f(x)^(g(x))=exp(In(f(x)^(g(x))))=exp(g(x)*Inf(x))
(f(x)^(g(x)))'=(exp(g(x)*Inf(x)))'=exp(g(x)*Inf(x))*(g(x)*Inf(x))'=f(x)^(g(x))*(g'(x)*Inf(x)+g(x)/f(x)*f'(x))

结果:
f(x)^(g(x))[g'(x)Lnf(x)+g(x)f'(x)/f(x)]