Differentiation — Maths STD 12 Science — Question

$y=\sin ^{-1}(3 x)+\sec ^{-1}\left(\frac{1}{3 x}\right)$
$\frac{d y}{d x}=\frac{d}{d x} \sin ^{-1}(3 x)+\frac{d}{d x} \sec ^{-1}\left(\frac{1}{3 x}\right)$
$\frac{d y}{d x}=\frac{3}{\sqrt{1-(3 x)^2}}+\frac{\frac{-1}{3 x^2}}{\frac{1}{3 x} \sqrt{\left(\frac{1}{(3 x)^2}-1\right)}}$
$\frac{d y}{d x}=\frac{3}{\sqrt{1-9 x^2}}-\frac{1}{\times \frac{\sqrt{\left(1-9 x^2\right)}}{3|x|}}$
$=\frac{3}{\sqrt{1-9 x^2}}-\frac{3|x|}{ X \sqrt{1-9 x^2}}$
$=\frac{3}{\sqrt{1-9 x^2}}\left(1-\frac{|X|}{X}\right)$
$=0 \quad X>0$
$=\frac{6}{\sqrt{1-9 x^2}} \quad x<0$