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

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

Answers (1)

Answer:

                (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

 

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