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If y2=Pxis a polynomial of degree 3 then 2ddxy3d2ydx2=

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a

P'''x+P'x

b

P''xP'''x

c

PxP'''x

d

Px−P'''x

answer is C.

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Detailed Solution

2ddxy3d2ydx2=2y3d3ydx3+3y2dydxd2ydx2=2y2yd2ydx3+3dydxd2ydx2→1y2=Px⇒2ydydx=P'x⇒2yd2ydx2+2dydx2=P"x⇒2yd3ydx3+2dydxd2ydx2+4dydxd2ydx2=P'''x⇒2yd3ydx3+6dydxd2ydx2=P'''x→2 ∴2ddxy3d2ydx3=y2P"'x=PxP"'x.

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