QJEEM24Maa4ab: JEE Main 2024 Mathematics - Class 12 JEEM24Maa4ab Solution: If , then at is equal to

$\begin{aligned}&\log _e y=3 \sin ^{-1} x\\&\begin{aligned}& y=e^{3 \sin ^{-1} x} \\& \frac{d y}{d x}=e^{3 \sin ^{-1} x} \cdot \frac{3}{\sqrt{1-x^2}}\end{aligned}\end{aligned}$

$\sqrt{1-x^2} \frac{d y}{d x}=3 y$

Again differentiate

$\begin{aligned}& \sqrt{1-x^2} \cdot y^{\prime \prime}-\frac{2 x}{2 \sqrt{1-x^2}} y^{\prime}=3 y^{\prime} \\& (1-x)^2 y^{\prime \prime}-x y^{\prime}=3 y^{\prime}\left(\sqrt{1-x^2}\right)\end{aligned}$

So value of $3 y^{\prime}\left(\sqrt{1-x^2}\right)$ at $x=\frac{1}{2}$

$\begin{aligned}& 3 \cdot \frac{3}{\sqrt{1-x^2}} e^{\sin ^{-1} x}\left(\sqrt{1-x^2}\right) \\& =9 e^{3 \frac{\pi}{6}}=9 e^{\frac{\pi}{2}}\end{aligned}$