Solveeit Logo
Login

Question

Mathematics Question on Differentiability

If y=sin⁡−11−x,y={{\sin }^{-1}}\sqrt{1-x}, then dydx\frac{dy}{dx} is equal to

A

11−x\frac{1}{\sqrt{1-x}}

B

−121−x\frac{-1}{2\sqrt{1-x}}

C

1x\frac{1}{\sqrt{x}}

D

−12x1−x\frac{-1}{2\sqrt{x}\sqrt{1-x}}

Answer

−12x1−x\frac{-1}{2\sqrt{x}\sqrt{1-x}}

Explanation

Solution

Given that, y=sin⁡−11−xy={{\sin }^{-1}}\sqrt{1-x}
Differentiating w.r.t. x,x, we have
dydx=11−(1−x).12.11−x.(−1)\frac{dy}{dx}=\frac{1}{\sqrt{1-(1-x)}}.\frac{1}{2}.\frac{1}{\sqrt{1-x}}.(-1)
=1x.(−1)21−x=\frac{1}{\sqrt{x}}.\frac{(-1)}{2\sqrt{1-x}}
=(−1)2x.1−x=\frac{(-1)}{2\sqrt{x}.\sqrt{1-x}}