If F(x) = \displaystyle \int0^{x^2} \cos(t)\, dt, then F'(x) =

2x \cos(x^2) By FTC and the chain rule, F'(x) = \cos(x^2)\cdot 2x = 2x\cos(x^2).

Fundamental Theorem of Calculus and Accumulation Functions

AP Calculus AB· difficulty 4/5

F(x) = \displaystyle \int_0^{x^2} \cos(t)\, dt

Explanation

F'(x) = \cos(x^2)\cdot 2x = 2x\cos(x^2)

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