Suppose with continuous on and differentiable on its domain

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Suppose

F(x)=\displaystyle\int_{5}^{g(x)} f(t)\,dt

with

f

continuous on

\mathbb R

and

g

differentiable on its domain. Which of the following expresses

F'(x)

in terms of

f

and

g

? (a)

f\bigl(g(x)\bigr)

(b)

f\bigl(g(x)\bigr)\,g'(x)

(c)

f'(g(x))\,g'(x)

(d)

f(x)\,g'(x)