1. Like this:

$=e^{3x}\left(\dfrac{1}{cos^2x}+3tgx\right)$

Factoring and differentiating are different verbs

2. I'm awful at math and my English is bad too . Thanks for help.

3. You're very welcome for my contributions.

4. If you're taking calculus, I wouldn't say you're all that terrible at math. A majority of people in the USA, at least, never take calculus, unfortunately.

5. $f(x)=e^{2\sqrt{x}}$
$f'(x)=(e^{2\sqrt{x}})'= (e^{2\sqrt{x}})' \cdot (2\sqrt{x})'= e^{2\sqrt{x}}\cdot \frac{1}{\sqrt{x}}= \frac{e^{2\sqrt{x}}}{\sqrt{x}}
$

I do it myself, so it's correct?

6. Looks good to me. However, I would recommend not introducing a new problem this far into a thread. It won't get the visibility that a new thread will.

7. I know that...
Anyway, I'm so happy that I understood this task.

8. Ok. Have a good one!

9. Correct!

EDIT: Oops, way way way too late =S

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