# Derivatives. Product rule with 3 products

1. Nov 21, 2007

### EvilBunny

1. The problem statement, all variables and given/known data

If f(x) = (3 x )(sin x) (cos x), find f'( x ).

A question I have is , is there anything special to do when you have 3 products instead of 2

3. The attempt at a solution

Well I used the product rule as if am multipling

(3xsinx) (cosx)

but that doesn't seem to get me the answer or maybe Its something about my answer because I put answers in a computer so sometimes its the notation.

here is my final answer
3sin(x)+cos(x)*3x*cos(x)-sin(x)(3x)sin(x)

2. Nov 21, 2007

### rock.freak667

well for 3 products...just take take the product of 2 terms and multiply by the differential of the of the 3rd term...if you dont get it

$$\frac{d}{dx}(UVW)=UV\frac{dW}{dx}+UW\frac{dV}{dx}+VW\frac{dU}{dx}$$

3. Nov 21, 2007

### EvilBunny

K managed to get it off of that thx

4. Aug 16, 2011

### jamball77

although the equation above is impressive and simple. I hate to learn yet another differentiation rule. your initial approach is correct.

(3xsinx) (cosx) = [(3x sinx) (-sin x)]+ [first ' * (cosx)]

the same old (first * second ') + (first ' * second) product rule.

now take derivative of (3x * sin x) with the product rule and plug it in where first' goes.

your computer probably does a better job of simplification than u :)

Last edited: Aug 16, 2011