If y = sin^-1x , then (1 - x^2)(d^2y)/(dx^2) is equal to

The correct answer is Option (2) → \(x\displaystyle\frac{dy}{dx}\)

Since \(y = \sin^{-1}x\),

    \( \displaystyle \frac{dy}{dx} = \frac{1}{\sqrt{1-x^2}} \)

so

    \( \displaystyle \sqrt{1-x^2}\,\frac{dy}{dx} = 1 \)

Differentiating again by the product rule:

    \( \displaystyle \sqrt{1-x^2}\,\frac{d^2y}{dx^2} - \frac{x}{\sqrt{1-x^2}}\,\frac{dy}{dx} = 0 \)

Multiplying by \(\sqrt{1-x^2}\):

    \( \displaystyle (1-x^2)\frac{d^2y}{dx^2} - x\frac{dy}{dx} = 0 \)

    \( \displaystyle (1-x^2)\frac{d^2y}{dx^2} = x\frac{dy}{dx} \)

NCERT (2026-27 edition):
Second Order Derivative