Given the parametric equations x=f(t),y=g(t), then d2ydx2 equals
A
d2ydt2.dxdt−dydtd2xdt2(dxdt)2
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B
dxdtd2ydt2−d2xdt2dydt(dxdt)3
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C
d2ydt2d2xdt2
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D
d2ydt2.dxdt−dydtd2xdt2(dxdt)
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Solution
The correct option is Bdxdtd2ydt2−d2xdt2dydt(dxdt)3 We have dydx=dydtdxdt ∴d2ydx2=ddt(dydtdxdt)dtdx =d2ydt2(dxdt)−(d2xdt2)dydt(dxdt)2×1dxdt =(dxdt).(d2ydt2)−(d2xdt2).(dydt)(dxdt)3.