Calc2.14

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Find the derivative of f(x)\, with respect to x\,: f(x)=\int _{{4}}^{{x^{2}}}\sin(e^{t})\,dt\,

This problem uses the Second Fundamental Theorem of Calculus but it also uses the Chain Rule. Since the upper limit of the integral is not plain x\,, then we must multiply by the derivative of the inside function just as we would in any other chain rule problem.

f'(x)=\sin(e^{{x^{2}}})(2x)\,

The \sin(e^{{x^{2}}})\, came from plugging the upper limit x^{2}\, into the inner function, f(t)\, and the 2x\, came from multiplying by the derivative of x^{2}\,.


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