$\frac{d}{d x}\left(\sin ^{-1}\left(3 x-4 x^3\right)\right), \frac{1}{2}

Question

$\frac{d}{d x}\left(\sin ^{-1}\left(3 x-4 x^3\right)\right), \frac{1}{2} < x < 1$ is

Aicharya · Accepted Answer

$\begin{aligned} & \frac{\mathrm{d}\left(\sin ^{-1}\left(3 \mathrm{x}-4 \mathrm{x}^3ight)ight)}{\mathrm{dx}} \ & =\frac{\mathrm{d}\left(\pi-3 \sin ^{-1} \mathrm{x}ight)}{\mathrm{dx}}\left[	ext { as } \frac{1}{2}<\mathrm{x}<1ight]=\frac{-3}{\sqrt{1-\mathrm{x}^2}}\end{aligned}$

$\frac{d}{d x}\left(\sin ^{-1}\left(3 x-4 x^3\right)\right), \frac{1}{2} < x < 1$ is

Solution