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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
)
where
f
′
(
t
)
≠
0
f'(t)\neq 0
f
′
(
t
)
=
0
, which expression represents
d
y
d
x
\dfrac{dy}{dx}
d
x
d
y
in terms of derivatives with respect to
t
t
t
? a)
d
x
d
t
d
y
d
t
\dfrac{\dfrac{dx}{dt}}{\dfrac{dy}{dt}}
d
t
d
y
d
t
d
x
b)
(
d
y
d
t
)
(
d
x
d
t
)
\left(\dfrac{dy}{dt}\right)\left(\dfrac{dx}{dt}\right)
(
d
t
d
y
)
(
d
t
d
x
)
c)
d
y
d
t
d
x
d
t
\dfrac{\dfrac{dy}{dt}}{\dfrac{dx}{dt}}
d
t
d
x
d
t
d
y
d)
g
(
t
)
f
(
t
)
\dfrac{g(t)}{f(t)}
f
(
t
)
g
(
t
)
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