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

[oridniv]

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]

Use the chain rule.

 

[cshum00]

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.

 

[oridniv]

thanx, makes much more sense

 

[mathwonk]

learn this rule: d/dx(e^u) = e^u (du/dx)

 

[theperthvan]

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

 

[HallsofIvy]

That's again the chain rule but with the two functions reversed!