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Mathematics
Mathematics
Problem
For a curve defined parametrically by
x
=
f
(
t
)
x=f(t)
x
=
f
(
t
)
and
y
=
g
(
t
)
y=g(t)
y
=
g
(
t
)
with
f
′
(
t
)
≠
0
f'(t)\neq 0
f
′
(
t
)
=
0
, which of the following equals
d
y
d
x
\dfrac{dy}{dx}
d
x
d
y
? a)
g
′
(
t
)
f
′
(
t
)
g'(t)\,f'(t)
g
′
(
t
)
f
′
(
t
)
b)
g
′
(
t
)
f
′
(
t
)
\dfrac{g'(t)}{f'(t)}
f
′
(
t
)
g
′
(
t
)
c)
f
′
(
t
)
g
′
(
t
)
\dfrac{f'(t)}{g'(t)}
g
′
(
t
)
f
′
(
t
)
d)
g
(
t
)
f
(
t
)
\dfrac{g(t)}{f(t)}
f
(
t
)
g
(
t
)
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