Question

-
sin
X
Ify=
dy
then (1-x²) equals-
dx
VI-X

Answer 1

$y = \frac{ {sin}^{ - 1}x }{ \sqrt{1 - {x}^{2} } } \\ \\ y \sqrt{1 - {x}^{2} } = {sin}^{ - 1} x \\ \\ differentiate \: \: \: w.r.t \: \: \: \: x \\ \\ y \frac{1}{2 \sqrt{1 - {x}^{2} } } ( - 2x) + \sqrt{1 - {x}^{2} } \frac{dy}{dx} = \frac{1}{ \sqrt{1 - {x}^{2} } } \\ \\ multiplying \: \sqrt{1 - {x}^{2} } both \: sides \\ \\ - xy + (1 - {x}^{2} ) \frac{dy}{dx} = 1 \\ \\ (1 - {x}^{2} ) \frac{dy}{dx} = 1 + xy$