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Question

Given the parametric equations x=f(t),y=g(t), then d2ydx2 equals

A
d2ydt2.dxdtdydtd2xdt2(dxdt)2
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B
dxdtd2ydt2d2xdt2dydt(dxdt)3
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C
d2ydt2d2xdt2
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D
d2ydt2.dxdtdydtd2xdt2(dxdt)
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Solution

The correct option is B dxdtd2ydt2d2xdt2dydt(dxdt)3
We have dydx=dydtdxdt
d2ydx2=ddt(dydtdxdt)dtdx
=d2ydt2(dxdt)(d2xdt2)dydt(dxdt)2×1dxdt
=(dxdt).(d2ydt2)(d2xdt2).(dydt)(dxdt)3.

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