#### Need solution for RD Sharma Maths Class 12 Chapter 11 Higher Order Derivatives Excercise Multiple Choice Questions Question 9

(a)

Hint:

We must know about the derivative of  $\sin^{-1} x$ .

Given:

$f(x)=\frac{\sin ^{-1} x}{\sqrt{1-x^{2}}}$ , then  $\left(1-x^{2}\right) f^{\prime}(x)-x f(x)=?$

Explanation:

$f(x)=\frac{\sin ^{-1} x}{\sqrt{1-x^{2}}}$

Differentiate with respect to $x$ ,

\begin{aligned} &y \sqrt{1-x^{2}}=\sin ^{-1} x \\ & \end{aligned}

$y \cdot \frac{1}{2 \sqrt{1-x^{2}}}(-2 x)+\sqrt{1-x^{2}} \frac{d y}{d x}=\frac{1}{\sqrt{1-x^{2}}} \\$

$-x y+\left(1-x^{2}\right) \frac{d y}{d x}=1$

Therefore,  $\left(1-x^{2}\right) f^{\prime}(x)-x f(x)=1$