How do I differentiate ${(e^e)}^x$?

Question

I know how to differentiate $e^x$ (it's just $e^x$), but how do I differentiate ${(e^e)}^x$?

any hints would be welcome.

If indeed you mean $e^{(e^x)}$, which is what $e^{e^x}$ means, then you want the chain rule. — vadim123, Jun 30 '14 at 14:17

score 5 · Accepted Answer · answered Jun 30 '14 at 14:15

5

Hint: write $(e^e)^x$ as $e^{ex}.$

Now use the fact that $\frac{d}{dx}[e^{kx}]=ke^{kx}$.

You may want to simplify your answer.

answered Jun 30 '14 at 14:15

beep-boop

score 2 · Answer 2 · answered Jun 30 '14 at 14:27

2

If $f(x)=c^x$ then $f'(x)=c^x\cdot\ln(c)$

So if $f(x)={(e^e)}^x$ then $f'(x)={(e^e)}^x\cdot\ln(e^e)={(e^e)}^x\cdot{e}$

answered Jun 30 '14 at 14:27

barak manos

2 Answers2