# Distributing the e term first

1. Aug 3, 2010

### justin345

1. The problem statement, all variables and given/known data
e3x(3sin x-cos x)

3. The attempt at a solution

e3x3(3sin x-cos x)+(3cos x+sin x)e3x=10e3xsin x.

Is that right?

2. Aug 3, 2010

### Staff: Mentor

Re: derivative

I don't think so, at least not the intermediate steps.

Could you try distributing the e term first, and then take the derivative of the two resulting terms, using the chain rule on each?

3. Aug 3, 2010

### justin345

Re: derivative

OK, so let me then get rid of parenthesis. I will show you my intermediate steps.

e3x3sinx-e3xcosx=
3e3xsinx+e3x3cosx-(3e3xcosx+e3x(-sinx))=
10e3xsin x

4. Aug 3, 2010

### Staff: Mentor

Re: derivative

I'm not seeing the chain rule being used. Remember, it's the first term multiplied by the derivative of the second term, plus the second term multiplied by the derivative of the first term....

http://en.wikipedia.org/wiki/Chain_rule

.

5. Aug 3, 2010

### Staff: Mentor

Re: derivative

Also, you should be careful to distinguish between the initial terms, and the derivative that you are solving for. Write it like this:

(e3x3sinx-e3xcosx)' =

Or

d/dx(e3x3sinx-e3xcosx) =

6. Aug 3, 2010

### justin345

Re: derivative

I am sorry, I don't quite understand what you are saying. I performed chain rule to the best of my knowledge. I don't know what else to do.

7. Aug 3, 2010

### lurflurf

Re: derivative

Don't worry about berkeman's confusing, unclear, and not helpful post. Your work is quite correct, but it may help to use a few more steps until you have more practice.

product rule
[e3x(3sin x-cos x)]'=(e3x)'(3sin x-cos x)+e3x(3sin x-cos x)'
chain rule and difference rule
=3e3x(3sin x-cos x)+e3x(3sin' x-cos' x)
distribute
=e3x(9sin x-3cos x)+e3x(3cos x+sin x)
gather like terms (exponential)
=e3x(9sin x-3cos x+3cos x+sin x)
gather like terms (sine and cosine)
=e3x(10sin x)
=10e3xsin x

8. Aug 3, 2010

### Staff: Mentor

Re: derivative

Sorry if I was confusing. Should I have been using the term product rule instead of the more general chain rule? It was the intermediate steps that I was trying to get laid out.

9. Aug 3, 2010

### Staff: Mentor

Re: derivative

Both rules need to be used in this problem. The product rule is used first, because the function is a product - e3x(3sin x-cos x). Then, to differentiate e3x, the chain rule is called for.

10. Aug 3, 2010

### justin345

Re: derivative

Does it mean that my calculation is correct?

11. Aug 3, 2010

### Staff: Mentor

Re: derivative

Yes.