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Find D 2 Y D X 2 Where Y = Log ( X 2 E 2 ) ? - Mathematics

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Question

Find \[\frac{d^2 y}{d x^2}\] where \[y = \log \left( \frac{x^2}{e^2} \right)\] ?

Solution

Here,

\[y = \log\left( \frac{x^2}{e^2} \right)\] 
\[\text { Differentiating  w . r . t .   x,   we  get }\] 
\[\frac{d y}{d x} = \frac{1}{\frac{x^2}{e^2}} \times \frac{2x}{e^2} = \frac{2}{x}\] 
\[\text { Differentiating  again  w . r . t .   x,   we  get }\] 
\[\frac{d^2 y}{d x^2} = \frac{- 2}{x^2}\] ?
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Chapter 12: Higher Order Derivatives - Exercise 12.1 [Page 17]

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RD Sharma Mathematics [English] Class 12
Chapter 12 Higher Order Derivatives
Exercise 12.1 | Q 30 | Page 17

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