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Mathematics
Mathematics
Problem
Explain in one sentence why, for a continuous function
f
f
f
and differentiable function
g
,
g,
g
,
the derivative of
F
(
x
)
=
∫
a
g
(
x
)
f
(
t
)
d
t
F(x)=\int_{a}^{g(x)} f(t)\,dt
F
(
x
)
=
∫
a
g
(
x
)
f
(
t
)
d
t
equals
f
(
g
(
x
)
)
g
′
(
x
)
.
f(g(x))\,g'(x).
f
(
g
(
x
))
g
′
(
x
)
.
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