# How do you find the derivative of #g(x) = int_3^x e^(4t²-t) dt# ?

Answering this question is one of the main jobs of the Fundamental Theorem of Calculus, Part I. (Its other main job is to help us prove the Fundamental Theorem of Calculus, Part II.)

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To find the derivative of ( g(x) = \int_{3}^{x} e^{4t^2 - t} , dt ), we can apply the Fundamental Theorem of Calculus. According to this theorem, if ( g(x) ) is defined as the integral from a constant (in this case, 3) to a variable (x) of a function (in this case, ( e^{4t^2 - t} )), then the derivative of ( g(x) ) with respect to ( x ) is simply the integrand evaluated at ( x ). Therefore, the derivative of ( g(x) ) is ( e^{4x^2 - x} ).

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