# Derivatives of exponentials (calc II)

1. Aug 31, 2011

### QuarkCharmer

1. The problem statement, all variables and given/known data
$$\frac{d}{dx}e^{ax^{3}}$$

I'm simply trying to determine whether or not I am doing these correctly and applying the chain rule properly.
2. Relevant equations
Chain rule et al.

3. The attempt at a solution

$\frac{d}{dx}e^{ax^{3}}$

$e^{ax^{3}}\frac{d}{dx}ax^{3}$

$e^{ax^{3}}a(3)x^{2}$

$3ae^{ax^{3}}x^{2}$

Does that look right to you? I am assuming "a" is just some constant, the book does not specify.

2. Aug 31, 2011

### vela

Staff Emeritus
Looks fine.

3. Aug 31, 2011

### bcsmith

Yes, this is correct. If you'd like proof take a look at (http://www.wolframalpha.com/input/?i=derivative+of+e^%28ax^3%29). "wolframalpha.com"[/URL] is a very good resource for checking your answers. Good luck!

Last edited by a moderator: Apr 26, 2017
4. Aug 31, 2011

### QuarkCharmer

Okay great!

$\frac{d}{dt}e^{tsin(2t)}$

$e^{tsin(2t)}\frac{d}{dt}tsin(2t)$

$e^{tsin(2t)}[sin(2t)+2cos(2t)]$

5. Aug 31, 2011

### vela

Staff Emeritus
Almost. The last term isn't correct.

6. Aug 31, 2011

### QuarkCharmer

Oh I think I just didn't type the "t". It's on my paper.

$e^{tsin(2t)}[sin(2t)+2tcos(2t)]$

Better?

7. Aug 31, 2011

### vela

Staff Emeritus
Ayuh.

8. Aug 31, 2011

### QuarkCharmer

Thanks a bunch!