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Mathematics
Mathematics
Problem
For differentiable functions
f
f
f
,
g
g
g
, and
h
h
h
, let
y
=
f
(
g
(
h
(
x
)
)
)
y = f\bigl(g\bigl(h(x)\bigr)\bigr)
y
=
f
(
g
(
h
(
x
)
)
)
. Which of the following expressions equals
d
y
d
x
\dfrac{dy}{dx}
d
x
d
y
? a)
f
′
(
g
(
h
(
x
)
)
)
g
′
(
h
(
x
)
)
f'(g(h(x)))\,g'(h(x))
f
′
(
g
(
h
(
x
)))
g
′
(
h
(
x
))
b)
f
′
(
g
(
x
)
)
g
′
(
h
(
x
)
)
h
′
(
x
)
f'(g(x))\,g'(h(x))\,h'(x)
f
′
(
g
(
x
))
g
′
(
h
(
x
))
h
′
(
x
)
c)
f
′
(
g
(
h
(
x
)
)
)
g
′
(
h
(
x
)
)
h
′
(
x
)
f'(g(h(x)))\,g'(h(x))\,h'(x)
f
′
(
g
(
h
(
x
)))
g
′
(
h
(
x
))
h
′
(
x
)
d)
f
′
(
g
(
h
(
x
)
)
)
g
′
(
x
)
h
′
(
x
)
f'(g(h(x)))\,g'(x)\,h'(x)
f
′
(
g
(
h
(
x
)))
g
′
(
x
)
h
′
(
x
)
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