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  • Provide Solution for RD Sharma Class 12 Chapter 11 Higher Order Derivatives Exercise Multiple Choice Question question 19

Provide Solution for RD Sharma Class 12 Chapter 11 Higher Order Derivatives Exercise Multiple Choice Question question 19

Answers (1)

Answer:

                (a)

Hint:

We must know about the derivative of x

Given:

                y=\frac{a x+b}{x^{2}+c} \

Explanation:

                y=\frac{a x+b}{x^{2}+c} \

                \begin{aligned} &\ &\left(x^{2}+c\right) y=a x+b \end{aligned}

Differentiate with respect to x

                2 x y+\left(x^{2}+c\right) \frac{d y}{d x}=a

Again differentiate,

                2 y+2 x y_{1}+2 x y_{1}+\left(x^{2}+c\right) y_{2}=0 \\

                \begin{aligned} &2 y+4 x y_{1}+\left(x^{2}+c\right) y_{2}=0 \end{aligned}

Differentiate again with respect to x

                2 y_{1}+4 y_{1}+4 x y_{2}+\left(x^{2}+c\right) y_{3}+2 x y_{2}=0 \\

                \begin{aligned} &6 y_{1}+6 x y_{2}+\left(x^{2}+c\right) y_{3}=0 \end{aligned}

                6 y_{1}+6 x y_{2}+\left(\frac{-2 y-4 x y_{1}}{y_{2}}\right) y_{3}=0 \\

                6 y_{1} y_{2}+6 x\left(y_{2}\right)^{2}-2 y-4 x y_{1} y_{3}=0 \\

                3 y_{1} y_{2}+3 x\left(y_{2}\right)^{2}-y-2 x y_{1} y_{3}=0

                \begin{aligned} \\ &\left(2 x y_{1}+y\right) y_{3}=\left(y_{1}+x y_{2}\right) 3 y_{2} \end{aligned}

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