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Mathematics
Problem
For differentiable functions
x
=
f
(
t
)
x=f(t)
x
=
f
(
t
)
and
y
=
g
(
t
)
y=g(t)
y
=
g
(
t
)
, which condition must hold at
t
=
t
0
t=t_0
t
=
t
0
so that
d
y
d
x
\dfrac{dy}{dx}
d
x
d
y
is defined at that point? a)
g
′
(
t
0
)
≠
0
g'(t_0)\neq 0
g
′
(
t
0
)
=
0
b)
f
′
(
t
0
)
=
g
′
(
t
0
)
f'(t_0)=g'(t_0)
f
′
(
t
0
)
=
g
′
(
t
0
)
c)
f
′
(
t
0
)
≠
0
f'(t_0)\neq 0
f
′
(
t
0
)
=
0
d)
f
(
t
0
)
≠
0
f(t_0)\neq 0
f
(
t
0
)
=
0
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