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Mathematics
Problem
If
y
=
cos
(
g
(
x
)
)
y=\cos(g(x))
y
=
cos
(
g
(
x
))
where
g
(
x
)
g(x)
g
(
x
)
is differentiable, which of the following represents
d
y
d
x
\dfrac{dy}{dx}
d
x
d
y
? a)
−
sin
(
g
(
x
)
)
-\sin\bigl(g(x)\bigr)
−
sin
(
g
(
x
)
)
b)
−
sin
(
g
(
x
)
)
g
′
(
x
)
-\sin\bigl(g(x)\bigr)\,g'(x)
−
sin
(
g
(
x
)
)
g
′
(
x
)
c)
sin
(
g
(
x
)
)
g
′
(
x
)
\sin\bigl(g(x)\bigr)\,g'(x)
sin
(
g
(
x
)
)
g
′
(
x
)
d)
−
sin
(
g
(
x
)
)
g
′
(
x
)
-\dfrac{\sin\bigl(g(x)\bigr)}{g'(x)}
−
g
′
(
x
)
sin
(
g
(
x
)
)
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