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Homework Help: Solving a derivative

  1. Jul 18, 2012 #1
    1. The problem statement, all variables and given/known data
    Find the derivativce of y=e^cosx*sinx

    2. Relevant equations

    3. The attempt at a solution

    i`m just unsure of whether e should be treated as e^x because its not that.. or if e should be treated like an f(x)a^x to f`(x)a^xlna, or if it is still considerd e^x.. here is my attempt.

    y`=e^cosx*(-sinx)*(sinx) + (cosx)(e^cosx)

    y`= e^cosx(cosx - sin^2x)
  2. jcsd
  3. Jul 18, 2012 #2


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    If you're differentiating y = (sin(x))ecos(x), then what you have done is fine.

    Writing ax as ex ln(a) can be helpful at times, but writing e in terms of some other constant generally isn't helpful when differentiating.
  4. Jul 18, 2012 #3

    Ah i just realised something... e^x = e^cosx in the sense that cosx is `x`. right?

    And also thank you for your help.
  5. Jul 18, 2012 #4


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    The chain rule. ##(f\circ g)'(x)=f'(g(x))g'(x)##
    The product rule. ##(fg)'(x)=f'(x)g(x)+f(x)g'(x)##

    Keep in mind that ##e^{f(x)}=exp(f(x))=(\exp\circ f)(x)##. So you will need the chain rule. You will also need the product rule to find f'(x).
  6. Jul 18, 2012 #5
    all right, thanks man.
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