Find derivative of complex sinusoidal function

pbonnie
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Homework Statement


Find derivative of:
h(x) = 3e^{sin(x+2)}


Homework Equations


chain rule of derivatives, product rule(?)


The Attempt at a Solution


I'm quite sure I'm doing this wrong. Because the exponent is a product, for the derivative of the exponent I would have to use the product rule? So:
h'(x) = sin(x+2)(3e^{sin(x+2)-1})(cos(x+2) + sin(1))

thank you for your help
 
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The exponent of 'e' is not a product, it is the sine function evaluated at (x+2). The derivative of the exponential function is not the same as x raised to a power.

Haven't you studied trig functions and the exponential function?
 
This is me attempting to get back into math after 5 years, I'm quite rusty, I'm relearning everything so I forget sometimes.
Okay, so then the derivative of the exponent of e would be
cos(x+2) ?
So it would be h′(x)=sin(x+2)(3e^{sin(x+2)−1})(cos(x+2)) ?
 
oh.. or just
h'(x) = 3e^{sin(x+2)}(cos(x+2))
Since it's of the form f(x) = a^{g(x)}?
 
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