NDA 2017 Maths · Mathematics · Derivatives · hard

If y=sin ^-1x, then (1-x^2(d^2y)/(dx^2-xdy/dx equals

Single correct option

y=\sin^{-1}x

, then

(1-x^2)\dfrac{d^2y}{dx^2}-x\dfrac{dy}{dx}

equals

Show answer and solution

Answer: (A) $0$

y'=\frac1{\sqrt{1-x^2}}

and

y''=\frac{x}{(1-x^2)^{3/2}}

. Then

(1-x^2)y''=\frac{x}{\sqrt{1-x^2}}=xy'

, so the expression is

xy'-xy'=0

. This is the standard identity for

\sin^{-1}x

; the other options come from sign slips in

y''

Original question written in the NDA 2017 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake