Let . What is…

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

Let F(x)=∫2x3+1(4t2−1) dtF(x)=\displaystyle\int_{2}^{x^{3}+1}\bigl(4t^{2}-1\bigr)\,dt. What is F′(x)F'(x) ? (a) 4(x3+1)2−14(x^{3}+1)^{2}-1 (b) (4x2−1) 3x2\bigl(4x^{2}-1\bigr)\,3x^{2} (c) (4(x3+1)2−1) 3x2\bigl(4(x^{3}+1)^{2}-1\bigr)\,3x^{2} (d) (4(x3+1)2−1) (x3+1)\bigl(4(x^{3}+1)^{2}-1\bigr)\,(x^{3}+1)

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