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Mathematics
Mathematics
Problem
Which expression equals
d
d
x
(
∫
g
(
x
)
h
(
x
)
f
(
t
)
d
t
)
\displaystyle \frac{d}{dx}\left(\int_{g(x)}^{h(x)} f(t)\,dt\right)
d
x
d
(
∫
g
(
x
)
h
(
x
)
f
(
t
)
d
t
)
where
f
f
f
is continuous and
g
,
h
g,h
g
,
h
are differentiable functions of
x
x
x
? a)
f
(
h
(
x
)
)
−
f
(
g
(
x
)
)
f\big(h(x)\big)-f\big(g(x)\big)
f
(
h
(
x
)
)
−
f
(
g
(
x
)
)
b)
(
h
′
(
x
)
−
g
′
(
x
)
)
f
(
x
)
(h'(x)-g'(x))\,f(x)
(
h
′
(
x
)
−
g
′
(
x
))
f
(
x
)
c)
f
(
h
(
x
)
)
h
′
(
x
)
−
f
(
g
(
x
)
)
g
′
(
x
)
f\big(h(x)\big)\,h'(x)-f\big(g(x)\big)\,g'(x)
f
(
h
(
x
)
)
h
′
(
x
)
−
f
(
g
(
x
)
)
g
′
(
x
)
d)
f
(
h
(
x
)
)
h
′
(
x
)
+
f
(
g
(
x
)
)
g
′
(
x
)
f\big(h(x)\big)\,h'(x)+f\big(g(x)\big)\,g'(x)
f
(
h
(
x
)
)
h
′
(
x
)
+
f
(
g
(
x
)
)
g
′
(
x
)
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