# 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?

Dec 13, 2016

Pose $f \left(x\right) = \ln x$ and $g \left(x\right) = {e}^{x}$

#### Explanation:

$x = \ln {e}^{x}$

$\frac{d}{\mathrm{dx}} \left(x\right) = \frac{d}{\mathrm{dx}} \left(\ln {e}^{x}\right)$

$1 = \frac{1}{e} ^ x \frac{d}{\mathrm{dx}} \left({e}^{x}\right)$

${e}^{x} = \frac{d}{\mathrm{dx}} \left({e}^{x}\right)$