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Question

If y2=P(x) be a cubic polynomial, then 2ddx(y3d2ydx2) is equal to

A
P′′′(x)+P(x)
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B
P′′(x)P′′′(x)
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C
P(x)P′′′(x)
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D
Constant
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Solution

The correct option is C P(x)P′′′(x)
y2=P(x)
P(x)=2yy
P′′(x)=2yy′′+2y2
P′′′(x)=2yy′′′+6yy′′
2ddx(y3y′′)=2[y3y′′′+3y2yy′′]
=y2[2yy′′′+6yy′′]
=P(x)P′′′(x).

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