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Question

If x=at2 and y=2at, then find d2ydx2.

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Solution

Given,
x=at2 and y=2at

On differentiating both sides w.r.t. t, we get,

dxdt=2at and dydt=2a

Therefore,
dydx=2a2at=1t


Now, d2ydx2=ddt(dydx)×dtdx

=ddt(1t)×12at=1t2×12at=12at3

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