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Mathematics
Mathematics
Problem
For a parametric curve given 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)\neq0
f
′
(
t
)
=
0
, which of the following is the correct expression for
d
y
d
x
\dfrac{dy}{dx}
d
x
d
y
in terms of
t
t
t
? a)
g
′
′
(
t
)
f
′
′
(
t
)
\dfrac{g''(t)}{f''(t)}
f
′′
(
t
)
g
′′
(
t
)
b)
f
′
(
t
)
g
′
(
t
)
\dfrac{f'(t)}{g'(t)}
g
′
(
t
)
f
′
(
t
)
c)
g
′
(
t
)
f
′
(
t
)
\dfrac{g'(t)}{f'(t)}
f
′
(
t
)
g
′
(
t
)
d)
g
(
t
)
f
(
t
)
\dfrac{g(t)}{f(t)}
f
(
t
)
g
(
t
)
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