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  • Please Solve RD Sharma Class 12 Chapter 11 Higher Order Derivatives Exercise Multiple Choice Questions Maths Textbook Solution Question 3

Please Solve RD Sharma Class 12 Chapter 11 Higher Order Derivatives Exercise Multiple Choice Questions Maths Textbook Solution Question 3

Answers (1)

Answer:

                (b)

Hint:

We must know the derivative of  x  and  y .

Given:

                \begin{aligned} &y=a x^{n+1}+b x^{-n} \\ \end{aligned}

Explanation:

                  \begin{aligned} &y=a x^{n+1}+b x^{-n} \\ \end{aligned}

                  \frac{d y}{d x}=(n+1) a x^{n+1-1}+(-n) b x^{-n-1} \\

                  \frac{d y}{d x}=(n+1) a x^{n}+(-n) b x^{-(n+1)}

                 \begin{aligned} &\frac{d^{2} y}{d x^{2}}=n(n+1) a x^{n-1}-n b x^{-(n+1)-1}(-(n+1)) \\ \end{aligned}

                 \frac{d^{2} y}{d x^{2}}=n(n+1) a x^{n-1}+n(n+1) b x^{-n-2}

                \begin{aligned} &x^{2} \frac{d^{2} y}{d x^{2}}=n(n+1)\left[a x^{n-1}+b x^{-(n+2)}\right] x^{2} \\ & \end{aligned}

               x^{2} \frac{d^{2} y}{d x^{2}}=n(n+1)\left[a x^{n-1+2}+b x^{-n-2+2}\right] \\

               x^{2} \frac{d^{2} y}{d x^{2}}=n(n+1)\left[a x^{n+1}+b x^{-n}\right]

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