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Partial Derivative of a Definite Integral

  1. Feb 25, 2016 #1
    I'm trying to find the partial derivatives of:
    f(x,y) = ∫ (from -4 to x^3y^2) of cos(cos(t))dt

    and I am completely lost, any help would be appreciated, thanks.
     
  2. jcsd
  3. Feb 25, 2016 #2

    fresh_42

    Staff: Mentor

    Calculate the integral, i.e. the anti-derivative of ##cos^2(t)##, substitute the boundaries and differentiate it.
     
  4. Feb 25, 2016 #3

    Mark44

    Staff: Mentor

    The integrand that zl99 wrote isn't ##\cos^2(t)## -- it's ##\cos(\cos(t))##.

    I'd say that the strategy here is to use a form of the Fundamental Theorem of Calculus; i.e., that ##\frac d {dt} \int_a^x f(t)~dt = f(x)##. In this problem, I think you need to involve the chain rule. I haven't worked the problem, but that's the way I would go.
     
  5. Feb 26, 2016 #4

    Ssnow

    User Avatar
    Gold Member

    yes as @Mark44 said you must before use the FTC (Fundamental Theorem of Calculus) and multiply by the partial derivatives of ##x^3y^2## in one case you obtain the partial derivative respect ##x## and in the other case respect ##y## (you will use the chain rule for this)
     
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