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Mathematics
Mathematics
Problem
Let
f
f
f
be continuous on an interval and let
g
g
g
be differentiable on the same interval. Determine
d
d
x
(
∫
g
(
x
)
7
f
(
t
)
d
t
)
\dfrac{d}{dx}\Bigl(\displaystyle \int_{g(x)}^{7} f(t)\,dt\Bigr)
d
x
d
(
∫
g
(
x
)
7
f
(
t
)
d
t
)
in terms of
f
f
f
,
g
g
g
, and
g
′
(
x
)
g'(x)
g
′
(
x
)
.
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