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Find derivative of complex sinusoidal function

  1. May 16, 2013 #1
    1. The problem statement, all variables and given/known data
    Find derivative of:
    [itex] h(x) = 3e^{sin(x+2)} [/itex]


    2. Relevant equations
    chain rule of derivatives, product rule(?)


    3. 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]
     
  2. jcsd
  3. May 16, 2013 #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?
     
  4. May 16, 2013 #3
    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] ?
     
  5. May 16, 2013 #4
    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]?
     
  6. May 16, 2013 #5

    SteamKing

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