CUET · MATHS · PYQ PAPER 2023
If \(y=\log \left[\frac{x^2}{e^2}\right]\) then value of \(\frac{d^2 y}{d x^2}\) is :
- A \(\frac{x^2}{e^4}\)
- B \(\frac{-2}{x^2}\)
- C \(\frac{e}{x^2}\)
- D \(2 x+\log 2\)
Answer & Solution
Correct Answer
(B) \(\frac{-2}{x^2}\)
Step-by-step Solution
Detailed explanation
\(y=2\log x - 2\) \(\frac{dy}{dx} = \frac{d}{dx}(2\log x - 2) = \frac{2}{x}\) \(\frac{d^2y}{dx^2} = \frac{d}{dx}\left(\frac{2}{x}\right) = -2x^{-2} = \frac{-2}{x^2}\)
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