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

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We must know about the derivative values of every function.


                y^{2}=a x^{2}+b x+c


                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


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