Chain Rule

**Truthbetold** · November 27th 2007, 07:45 PM

Let s = cos (theta). Evaluate ds/dt when theta= $\frac {3pi}{2}$ and dtheta/dt= 5.

I have no clue what they want me to do.
The answer is 5

**earboth** · November 27th 2007, 08:40 PM

Originally Posted by Truthbetold

Let s = cos (theta). Evaluate ds/dt when theta= $\frac {3pi}{2}$ and dtheta/dt= 5.

Hello,

you have:

$s=\cos(\theta)$ . Now derivate wrt t. Use chain rule!:

$\frac{ds}{dt}=-\sin(\theta) \cdot \frac{d \theta}{dt}$

Plug in the values you know:

$\frac{ds}{dt}=-\sin\left(\frac {3\pi}{2} \right) \cdot 5$

Since $-\sin\left(\frac {3\pi}{2} \right) = 1$ the result is 5.

**Truthbetold** · November 27th 2007, 08:51 PM

Originally Posted by earboth

Hello,

you have:

$s=\cos(\theta)$ . Now derivate wrt t. Use chain rule!:

$\frac{ds}{dt}=-\sin(\theta) \cdot \frac{d \theta}{dt}$

Plug in the values you know:

$\frac{ds}{dt}=-\sin\left(\frac {3\pi}{2} \right) \cdot 5$

Since $-\sin\left(\frac {3\pi}{2} \right) = 1$ the result is 5.

Ooooooh! I see.
It threw me off that the derivative of 3pi/2 equaled 5.
Makes sense now.

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