If $\log_e y=3\sin^{-1}x$, then $(1-x^2)y''-xy'$ at $x=\frac{1}{2}$ is equal to

JEE Main 2024 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 9 April 2024, Shift 2, Maths Q8

Question 8 of 90 in this shift, Maths question 8 of 30, Section A.

\log_e y=3\sin^{-1}x

, then

(1-x^2)y''-xy'

x=\frac{1}{2}

is equal to

(1) $9e^{\pi/2}$ Official answer
(2) $9e^{\pi/6}$
(3) $3e^{\pi/2}$
(4) $3e^{\pi/6}$

Official answer

Option 1

NTA final key.

Chapter: Continuity and Differentiability
Topic: Chain Rule
Idea tested: Second Order Implicit Chain Rule

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Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 42 of the 174 JEE Main shifts held from 2017 to 2026.