JEE Main 2022 · 27 Jun · Shift 2 · Mathematics Q26

MathematicsInteger+4 / -1Question 26 of 90

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

Your answer

Answer and worked solution

Official answer: 16

Derivatives. $y=x^{x^2}$ , $\ln y=x^2\ln x$ : at $x=1$ , $y=1$ , $y'=1$ , and $y''=4$ .

Inverse. $\dfrac{d^2x}{dy^2}=-\dfrac{y''}{(y')^3}=-4$ , so the value is $16$ .

Answer: 16

JEE Main 2022 · 27 Jun · Shift 2, Mathematics question 26