determine the derivative of $\displaystyle y=3e^{sin(x+2)}$

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- Sep 1st 2010, 10:42 AMeuclid2derivative 3
determine the derivative of $\displaystyle y=3e^{sin(x+2)}$

- Sep 1st 2010, 11:15 AMArchie Meade
- Sep 4th 2010, 06:38 AMeuclid2
is this the chain rule? i'm not familiar with the chain rule is there another way to do it?

- Sep 4th 2010, 07:04 AMe^(i*pi)
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 $\displaystyle u = \sin(x+2)$ then you can find $\displaystyle \frac{du}{dx}$ 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 $\displaystyle y = 3e^u$ which you should know how to solve.

I must stress that this is still the chain rule though - Sep 4th 2010, 11:47 AMeuclid2
ok so:

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

correct ? - Sep 4th 2010, 11:51 AMHallsofIvy
Except for the wrong number of left parentheses on ((sin(x+ 2)), yes, it is correct.

See, isn't the chain rule nice?