CUET · MATHS · PYQ PAPER 2023
If \(y=\frac{\log x}{x^2}\), then find \(\frac{d^2 y}{d x^2}\).
- A \(\frac{5 \log x-6}{x^3}\)
- B \(\frac{3 \log x-2}{x^2}\)
- C \(\frac{4 \log x-3}{x}\)
- D \(\frac{6 \log x-5}{x^4}\)
Answer & Solution
Correct Answer
(D) \(\frac{6 \log x-5}{x^4}\)
Step-by-step Solution
Detailed explanation
\( \frac{dy}{dx} = \frac{\frac{1}{x} \cdot x^2 - \log x \cdot 2x}{(x^2)^2} = \frac{x - 2x \log x}{x^4} = \frac{1 - 2 \log x}{x^3} \) \( \frac{d^2y}{dx^2} = \frac{(-\frac{2}{x})x^3 - (1 - 2 \log x)(3x^2)}{(x^3)^2} \)…
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