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  • Explain solution RD Sharma class 12 Chapter 11 Higher Order Derivatives exercise Fill in the blanks question 6

Explain solution RD Sharma class 12 Chapter 11 Higher Order Derivatives exercise Fill in the blanks question 6

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Answer:  \frac{d^{2} y}{d x^{2}}=\frac{-1}{x^{2}}

Hint: Differentiate y w.r.t x twice to get  \frac{d^{2} y}{d x^{2}}.

Given:  y=\log _{e} x

Solution:

It is given that: y=\log _{e} x

\therefore \frac{d y}{d x}=\frac{1}{x}

Again, differentiating w.r.t x:

\begin{aligned} &\frac{d^{2} y}{d x^{2}}=\frac{-1}{x^{2}} \\ & \end{aligned}

Thus, 2 \frac{d^{2} y}{d x^{2}}=\frac{-1}{x^{2}} ..

 

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