chain rule derivatives...

**mathaction** · October 3rd 2007, 07:16 PM

y(

) = e

sin(8

)

for this one i got 8e^(theta)*cos(8theta)...

but it was wrong, what did i do wrong??

**TKHunny** · October 3rd 2007, 07:22 PM

You have neglected the fact that there is a product of functions.

If f(x) = g(x)*h(x), then f'(x) = g(x)*h'(x) + g'(x)*h(x).

Ringing any bells?

**mathaction** · October 3rd 2007, 07:45 PM

Originally Posted by TKHunny

You have neglected the fact that there is a product of functions.

If f(x) = g(x)*h(x), then f'(x) = g(x)*h'(x) + g'(x)*h(x).

Ringing any bells?

can you do it for me so i can see...

**Soroban** · October 3rd 2007, 07:59 PM

Hello, mathaction!

Have you forgotten the Product Rule?

$y \:=\:e^{\theta}\!\cdot\!\sin(8\theta)$

We have: . $\frac{dy}{d\theta} \;=\;e^{\theta}\cdot\cos(8\theta)\cdot8 + e^{\theta}\cdot\sin(\theta) \;=\;e^{\theta}\left[8\cos(8\theta) + \sin(\theta)\right]$

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