CUET · MATHS · PYQ PAPER 2023
If \(x=e^y+e^y+\cdots\) to \(\infty, x>0\) then \(\frac{d^2 y}{d x^2}\) is:
- A \(-x^2\)
- B \(-\frac{1}{x^2}\)
- C \(\frac{1}{x^2}\)
- D \(x^2\)
Answer & Solution
Correct Answer
(B) \(-\frac{1}{x^2}\)
Step-by-step Solution
Detailed explanation
\(x = e^{y+x}\) \(\ln x = y+x\) \(\frac{1}{x} = \frac{dy}{dx} + 1\) \(\frac{dy}{dx} = \frac{1}{x} - 1\) \(\frac{d^2 y}{d x^2} = -\frac{1}{x^2}\)
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