If $x y=a x^2+(b / x)$, then $ x \frac{d^2 y}{d x^2}+2 \frac{d y}{d x}= $

JEE MATHEMATICS MCQ: DIFFERENTIATION

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Application +4 | -1

x y=a x^2+(b / x)

, then

x \frac{d^2 y}{d x^2}+2 \frac{d y}{d x}=

View answer and explanation

Correct option: C

\frac{2 y}{x}

Option C (

\frac{{2 y}}{{x}}

) is correct because after differentiating the given equation twice and simplifying, the expression

x \frac{{d^2 y}}{{d x^2}}+2 \frac{{d y}}{{d x}}

simplifies to

\frac{{2 y}}{{x}}

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