**Finding Partial Derivatives from an Integral (Larson 9e 13.3.39)**

Here’s a problem (13.3.39, p. 914) from Larson et al.’s 9^{th} edition of Calculus:

Here, you can find partial derivatives once you solve for the definite integral. In the *x* world, the *y* terms become 0, and the only difficulty is noting the double negative that results in the partial derivative with respect to *x* being -*x*^{2} +1 rather than -*x*^{2} -1. Don’t be thrown off by the appearance of a definite integral in a basic problem of this kind. Simply solve the definite integral first.

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