## Wondermath 4 years ago What's the derivative of the following? (I will draw it)

1. Wondermath

|dw:1335940380736:dw|

2. Wondermath

is it e^(x/2)ln2

3. anonymous

1/2e^1/2x

4. anonymous

I think it's only $$\LARGE \frac{e^{x/2}}{2}$$ Isn't it? It can be rewritten as e^(x/2)

5. Wondermath

can u tell me how you got it?

6. anonymous

Rewrite it as $e^\frac{x}{2}$Then the derivative of e^u is e^u u', right? So we have derivative of that = e^(x/2) * d(x/2) = 1/2 :-)

7. anonymous

$\huge (\sqrt{e})^x=(e^{1/2})^x=e^{x/2}$ Apply chain rule to get $\huge e^{x/2} \over\huge 2$

8. kropot72

$(\sqrt{e})^{x}=(e ^{1/2})^{x}=e ^{x/2}$

9. anonymous

|dw:1335940696779:dw|

10. thomas5267

The winner of the LaTeX speed competition is...@bmp ! Congratulations!

11. Wondermath

thanks guys :)