Question

if y=sin^-1x then find dy/dx is :​

Answer 1

$y = sin {}^{ - 1} x$

$siny = x \: \: \: \: \: \: \: \: \: - (1)$

Apply differentiation

$cosy \frac{dy}{dx} = 1$

$\frac{dy}{dx} = \frac{1}{cosy}$

$\frac{dy}{dx} = \frac{1}{ \sqrt{1 - sin {}^{2} y} }$

$\frac{dy}{dx} = \frac{1}{ \sqrt{1 - x {}^{2} } }$