# Derivative of e^x=e^x, the derivative of e^2x doesn't equal e^2x

I have a test tomorrow so I may keep asking questions frequently. For now, why is it that when the derivative of e^x=e^x, the derivative of e^2x doesn't equal e^2x. I've been looking for the rule but can't find it anywhere.

cristo
Staff Emeritus
Use the chain rule.

derivative of
e^x = (1)(e^x)
the 1 comes from the derivative of x because of chain rule

derivative of
e^2x = (2)(e^2x)
the 2 comes from the derivative of 2x because of chain rule

correct me if i am wrong.

Last edited:
thanx, makes much more sense

mathwonk
Homework Helper
2020 Award
learn this rule: d/dx(e^u) = e^u (du/dx)

$$e^{2x}=[e^x]^2$$
Since $$\frac{d}{dx}f(x)^n = nf'(x){f(x)}^{n-1}$$
then if $$f(x)=e^{2x}$$ ...go from there.

HallsofIvy