If $y(x)=\left(x^x\right)^x$, $x>0$, then $\frac{d^2x}{dy^2}+20$ at $x=1$ is equal to ___________.

JEE Main 2022 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 27 June 2022, Shift 2, Maths Q26

Question 26 of 90 in this shift, Maths question 26 of 30, Section B.

y(x)=\left(x^x\right)^x

x>0

, then

\frac{d^2x}{dy^2}+20

x=1

is equal to ___________.

Official answer

NTA final key.

Chapter: Continuity and Differentiability
Topic: Chain Rule
Idea tested: Logarithmic Differentiation for Power Towers

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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 108 of the 174 JEE Main shifts held from 2017 to 2026.