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Mathematics
Mathematics
Problem
If
x
=
f
(
t
)
x = f(t)
x
=
f
(
t
)
and
y
=
ϕ
(
t
)
y = \phi(t)
y
=
ϕ
(
t
)
, prove that
d
2
y
d
x
2
=
f
0
2
−
f
1
f
2
f
1
3
\frac{d^2 y}{dx^2} = \frac{f_0^2 - f_1 f_2}{f_1^3}
d
x
2
d
2
y
=
f
1
3
f
0
2
−
f
1
f
2
, where suffixes denote differentiation w.r.t.
t
t
t
.
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