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  • Provide Solution for RD Sharma Class 12 Chapter 11 Higher Order Derivatives Exercise Multiple Choice Question Question 28

Provide Solution for RD Sharma Class 12 Chapter 11 Higher Order Derivatives Exercise Multiple Choice Question Question 28

Answers (1)

Answer:

                (d)

Hint:

We must know about the derivative rules of logarithm.

Given:

                y=\log _{e}\left(\frac{x^{2}}{e^{2}}\right)

Explanation:

                y=\log _{e}\left(\frac{x^{2}}{e^{2}}\right)

Differentiate with respect to  x

                \frac{d y}{d x}=\frac{1}{\frac{x^{2}}{e^{2}}} \cdot \frac{1}{e^{2}} 2 x

                \begin{aligned} &\\ &\frac{d y}{d x}=\frac{2}{x} \end{aligned}

Again differentiate,

                \frac{d^{2} y}{d x^{2}}=2\left(\frac{-1}{x^{2}}\right)

                \begin{aligned} & \\ &\frac{d^{2} y}{d x^{2}}=\frac{-2}{x^{2}} \end{aligned}

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