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Mathematics
Mathematics
Problem
Suppose
F
(
x
)
=
∫
5
g
(
x
)
f
(
t
)
d
t
F(x)=\displaystyle\int_{5}^{g(x)} f(t)\,dt
F
(
x
)
=
∫
5
g
(
x
)
f
(
t
)
d
t
with
f
f
f
continuous on
R
\mathbb R
R
and
g
g
g
differentiable on its domain. Which of the following expresses
F
′
(
x
)
F'(x)
F
′
(
x
)
in terms of
f
f
f
and
g
g
g
? a)
f
(
g
(
x
)
)
f\bigl(g(x)\bigr)
f
(
g
(
x
)
)
b)
f
(
g
(
x
)
)
g
′
(
x
)
f\bigl(g(x)\bigr)\,g'(x)
f
(
g
(
x
)
)
g
′
(
x
)
c)
f
′
(
g
(
x
)
)
g
′
(
x
)
f'(g(x))\,g'(x)
f
′
(
g
(
x
))
g
′
(
x
)
d)
f
(
x
)
g
′
(
x
)
f(x)\,g'(x)
f
(
x
)
g
′
(
x
)
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