# derivative 3

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• Sep 1st 2010, 11:42 AM
euclid2
derivative 3
determine the derivative of $y=3e^{sin(x+2)}$
• Sep 1st 2010, 12:15 PM
Archie Meade
Quote:

Originally Posted by euclid2
determine the derivative of $y=3e^{sin(x+2)}$

$u=x+2$

$v=sinu$

$w=e^v$

$y=3w$

$\displaystyle\frac{dy}{dx}=\frac{dy}{dw}\, \frac{dw}{dv}\, \frac{dv}{du}\, \frac{du}{dx}$
• Sep 4th 2010, 07:38 AM
euclid2
is this the chain rule? i'm not familiar with the chain rule is there another way to do it?
• Sep 4th 2010, 08:04 AM
e^(i*pi)
Quote:

Originally Posted by euclid2
is this the chain rule? i'm not familiar with the chain rule is there another way to do it?

Yes that is the chain rule and it's the only way to solve this question.

Archie Meade's way is best

If you let $u = \sin(x+2)$ then you can find $\frac{du}{dx}$ without much difficulty (although you're using the chain rule the derivative of x is 1 so it makes no numerical difference in this case)

Thus you have $y = 3e^u$ which you should know how to solve.

I must stress that this is still the chain rule though
• Sep 4th 2010, 12:47 PM
euclid2
ok so:

f '(x) = 3 * cos(x + 2) * e ^ ((sin(x + 2))

correct ?
• Sep 4th 2010, 12:51 PM
HallsofIvy
Except for the wrong number of left parentheses on ((sin(x+ 2)), yes, it is correct.

See, isn't the chain rule nice?