CUET · MATHS · PYQ PAPER 2023
If \(y=x^2 \log x\) then \(\frac{d^2 y}{d x^2}=\)
- A \(\left(x^2+2 x+1\right) \log x\)
- B \(\log \left(3 e x^2\right)\)
- C \(\log \left(x+x^2\right)\)
- D \(\log \left(e^3 x^2\right)\)
Answer & Solution
Correct Answer
(D) \(\log \left(e^3 x^2\right)\)
Step-by-step Solution
Detailed explanation
\(\frac{dy}{dx} = x^2 \cdot \frac{1}{x} + 2x \log x = x + 2x \log x\) \(\frac{d^2 y}{d x^2} = 1 + 2 \cdot \log x + 2x \cdot \frac{1}{x}\) \(\frac{d^2 y}{d x^2} = 1 + 2 \log x + 2 = 2 \log x + 3\) \(\frac{d^2 y}{d x^2} = \log x^2 + \log e^3 = \log (e^3 x^2)\)
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