# Homework Help: Product Rule of x = r cos()

1. Mar 31, 2010

### TheDoorsOfMe

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

r = r(t)
$$\theta$$ = $$\theta$$(t)

x = r cos($$\theta$$)

dx/dt =dr/dt cos($$\theta$$) - r sin($$\theta$$) d$$\theta$$/dt

3. The attempt at a solution

Where does the d$$\theta$$/dt come from at the end of the derivative? I know I'm using product rule here because r and theta are both functions of t. But, the derivative of cos is just -sin. Why would there be a d$$\theta$$/dt at the end?

2. Mar 31, 2010

### gabbagabbahey

No, $\frac{d}{d\theta}\cos\theta=-\sin\theta$ but $\frac{d}{dt}\cos\theta=\left(\frac{d}{d\theta}\cos\theta\right)\left(\frac{d\theta}{dt}\right)$ via the chain rule.

3. Mar 31, 2010

### Staff: Mentor

Chain rule.
d/dt(cos(theta)) = -sin(theta)*d(theta)/dt

4. Mar 31, 2010

### TheDoorsOfMe

oooooooooooooohhhhhhhhhhhh! man I'm kinda disappointed I didn't see that one : ( oh well. Thank very much guys!