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 April 7th, 2013, 09:16 PM #1 Senior Member   Joined: Jul 2012 Posts: 225 Thanks: 0 Multivariable calculus - partial derivatives Hey, can anyone please explain to me how do I find the derivative of an integral? obviously they cancel each other out, but how do the integration limits play a role? here's the question: find the partial derivatives (first partial derivatives, only derive once) of the function: $f(x,y)=\int_\pi^{x^2+y^2}sin(t^{2})dt$ find: $\frac{df}{dx} f(x,y)$ and $\frac{df}{dy}f(x,y)$
April 8th, 2013, 01:12 PM   #2
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Re: Multivariable calculus - partial derivatives

Quote:
 Originally Posted by OriaG Hey, can anyone please explain to me how do I find the derivative of an integral? obviously they cancel each other out, but how do the integration limits play a role? here's the question: find the partial derivatives (first partial derivatives, only derive once) of the function: $f(x,y)=\int_\pi^{x^2+y^2}sin(t^{2})dt$ find: $\frac{df}{dx} f(x,y)$ and $\frac{df}{dy}f(x,y)$
Let $g(u)=\int_\pi^usin(t^{2})dt$
Then ?f/?x = (dg/du)(?u/?x) = $2xsin(u^{2})$, where $u=x^{2} + y^{2}$

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