# Product Rule of x = r cos()

## Homework Statement

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

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

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

## 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?

## Answers and Replies

gabbagabbahey
Homework Helper
Gold Member
. But, the derivative of cos is just -sin. Why would there be a d$$\theta$$/dt at the end?

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.

Mark44
Mentor

## Homework Statement

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

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

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

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

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