# Solving a derivative

1. Jul 18, 2012

### Plutonium88

1. The problem statement, all variables and given/known data
Find the derivativce of y=e^cosx*sinx

2. Relevant equations

3. The attempt at a solution

im just unsure of whether e should be treated as e^x because its not that.. or if e should be treated like an f(x)a^x to f(x)a^xlna, or if it is still considerd e^x.. here is my attempt.

y=e^cosx*(-sinx)*(sinx) + (cosx)(e^cosx)

y= e^cosx(cosx - sin^2x)

2. Jul 18, 2012

### SammyS

Staff Emeritus

If you're differentiating y = (sin(x))ecos(x), then what you have done is fine.

Writing ax as ex ln(a) can be helpful at times, but writing e in terms of some other constant generally isn't helpful when differentiating.

3. Jul 18, 2012

### Plutonium88

Ah i just realised something... e^x = e^cosx in the sense that cosx is x. right?

And also thank you for your help.

4. Jul 18, 2012

### Fredrik

Staff Emeritus
The chain rule. $(f\circ g)'(x)=f'(g(x))g'(x)$
The product rule. $(fg)'(x)=f'(x)g(x)+f(x)g'(x)$

Keep in mind that $e^{f(x)}=exp(f(x))=(\exp\circ f)(x)$. So you will need the chain rule. You will also need the product rule to find f'(x).

5. Jul 18, 2012

### Plutonium88

all right, thanks man.