Find derivative of complex sinusoidal function

[pbonnie]

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:
$h'(x) = sin(x+2)(3e^{sin(x+2)-1})(cos(x+2) + sin(1))$

$thank you for your help$

 

[SteamKing]

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?

 

[pbonnie]

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 $h′(x)=sin(x+2)(3e^{sin(x+2)−1})(cos(x+2))$ ?

 

[pbonnie]

oh.. or just
$h'(x) = 3e^{sin(x+2)}(cos(x+2))$
Since it's of the form $f(x) = a^{g(x)}$?

 

[SteamKing]

e^u has its own rule for derivative. If y = e^u, then dy/dx = e^u * du/dx

a^u has a separate rule.

Brush up on your derivative rules: http://en.wikipedia.org/wiki/Table_of_derivatives