Question

请问x的5x次方这样的幂指函数如何求导?

Answer 1

就用一下对数恒等式就可以了,

x^5x=(e^lnx)^5x=e^(5x *lnx)

所以

(x^5x)'

=[e^(5x *lnx)]'

=e^(5x *lnx) * (5x *lnx)'

=x^5x * (5lnx +5x *1/x)

=x^5x *(5lnx+5)