Find derivative of complex sinusoidal function

  • Thread starter pbonnie
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  • #1
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Homework Statement


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


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:
[itex] h'(x) = sin(x+2)(3e^{sin(x+2)-1})(cos(x+2) + sin(1)) [/itex]

[itex] thank you for your help [/itex]
 

Answers and Replies

  • #2
SteamKing
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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?
 
  • #3
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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
[itex] cos(x+2) [/itex] ?
So it would be [itex] h′(x)=sin(x+2)(3e^{sin(x+2)−1})(cos(x+2))[/itex] ?
 
  • #4
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oh.. or just
[itex] h'(x) = 3e^{sin(x+2)}(cos(x+2))[/itex]
Since it's of the form [itex] f(x) = a^{g(x)}[/itex]?
 
  • #5
SteamKing
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