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Mathematics
Problem
For the parametric equations
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
, the expression for the first derivative
d
y
d
x
\dfrac{dy}{dx}
d
x
d
y
is a)
d
y
d
t
d
x
d
t
\dfrac{dy}{dt}\,\dfrac{dx}{dt}
d
t
d
y
d
t
d
x
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
)
g'(t)-f'(t)
g
′
(
t
)
−
f
′
(
t
)
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