Let f (x) be differentiable, find the function y = f (e ^ x) e ^ f (x), and find the derivative of the independent variable x

Let f (x) be differentiable, find the function y = f (e ^ x) e ^ f (x), and find the derivative of the independent variable x

Derivation of compound function
y '=[f(e^x)]'e^f(x)+f(e^x)·[e^f(x)] '
=f '(e^x)·e^x·e^f(x)+f(e^x)·e^f(x)·f '(x)