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  • Please Solve RD Sharma Class 12 Chapter 11 Higher Order Derivatives Exercise Multiple Choice Questions Maths Textbook Solution Question 26

Please Solve RD Sharma Class 12 Chapter 11 Higher Order Derivatives Exercise Multiple Choice Questions Maths Textbook Solution Question 26

Answers (1)

Answer:

                (a)

Hint:

We must know about the derivative values of every function.

Given:

                y^{2}=a x^{2}+b x+c

Explanation:

                y^{2}=a x^{2}+b x+c

                \\ 2 y \frac{d y}{d x}=2 a x+b

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

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

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

                y \frac{d^{2} y}{d x^{2}}=\frac{4 a y^{2}-(2 a x+b)^{2}}{4 y^{2}} \

                \begin{aligned} &\ &4 y^{3} \frac{d^{2} y}{d x^{2}}=4 a\left(a x^{2}+b x+c\right)-\left(4 a^{2} x^{2}+4 a x b+b^{2}\right) \end{aligned}

                4 y^{3} \frac{d^{2} y}{d x^{2}}=4 a c-b^{2} \

                \begin{aligned} &\ &y^{3} \frac{d^{2} y}{d x^{2}}=\frac{4 a c-b^{2}}{4} \end{aligned}        

                                = Constant

 

Posted by

infoexpert27

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