Partial Derivative of Definite Integral: int[-4, x^3y^2] cos(cos t) dt at (pi, 1)

zl99

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I think I know how to do this question but I'm stuck on finding the partial derivatives of this integral:.

\(\displaystyle \mbox{Compute the maximal rate of change in }\, f\, (x,\, y)\, =\, \)

. . .\(\displaystyle \displaystyle \int_{-4}^{x^3\, y^2}\, \cos\,\left(\cos\, t\right)\, dt\, \mbox{ at the point }\, \left(\pi,\, 1\right).\)

Thanks in advance!
 

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Extrems of an integral function

Hello,

you only need the 1st theorem of Calculus, which gives us the relationship between integration and derivation:

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in our case, we have a two variables function, so we can do two partial derivatives:

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Applying the chain rule for derivatives:

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The other partial derivative has the same process of calculus. Hope this can help.

Regards
 

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