JEE Advance - Mathematics (1988 - No. 26)
If $${y^2} = P\left( x \right)$$, a polynomial of degree $$3$$, then $$2{d \over {dx}}\left( {{y^3}{{{d^2}y} \over {d{x^2}}}} \right)$$ equals
$$P''\left( x \right) + P\left( x \right)$$
$$P'\left( x \right)P''\left( x \right)$$
$$P\left( x \right)P''\left( x \right)$$
a constant