`F(x) = int_(x)^(x^2)(e^(t^2))dt` Find the derivative of the function.

Textbook Question

Chapter 5, 5.3 - Problem 57 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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gsarora17 | (Level 2) Associate Educator

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`F(x)=int_x^(x^2)(e^(t^2))dt`

From the fundamental theorem of calculus,

`int_x^(x^2)(e^(t^2))dt=F(x^2)-F(x)`

`d/dxint_x^(x^2)(e^(t^2))dt=F'(x^2).d/dx(x^2)-F'(x)`

`=2x(e^((x^2)^2))-e^(x^2)`

`=2x(e^(x^4))-e^(x^2)`

 

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