if you=at^2, x=2at d^2y/dx^2 at x=1/2
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Class 12
>>Maths
>>Continuity and Differentiability
>>Derivatives of Implicit Functions
>>If x = at^2 and y = 2at , then find d^2
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If x=at
2
and y=2at, then find
dx
2
d
2
y
.
Medium
Solution
verified
Verified by Toppr
Given,
x=at
2
and y=2at
On differentiating both sides w.r.t. t, we get,
dt
dx
=2at and
dt
dy
=2a
Therefore,
dx
dy
=
2at
2a
=
t
1
Now,
dx
2
d
2
y
=
dt
d
(
dx
dy
)×
dx
dt
=
dt
d
(
t
1
)×
2at
1
=−
t
2
1
×
2at
1
=−
2at
3
1
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