Question

If f is the inverse of g, then we know that f(g(x))=x, how do you use this fact to derive the derivative formula dy/dx e^x= e^x?

Answer 1

Pose `f(x) = lnx` and `g(x) = e^x`

Explanation:

`x=lne^x`

`d/(dx) (x) = d/(dx) (lne^x)`

`1 = 1/e^x d/(dx)(e^x)`

`e^x = d/(dx)(e^x)`