AP EAMCET · Maths · Differentiation
If \(y=\frac{\log x}{x}\), then \(\frac{d^2 y}{d x^2}\) at \(x=1\)
- A \(-e^{-3}\)
- B \(-3\)
- C \(3\)
- D \(e^3\)
Answer & Solution
Correct Answer
(B) \(-3\)
Step-by-step Solution
Detailed explanation
\(y=\frac{\log x}{x}\) \(\Rightarrow \quad x y=\log x\) \(\Rightarrow \quad x \frac{d y}{d x}+y=\frac{1}{x}\)...(i) \(\Rightarrow \quad \frac{d y}{d x}=\left(\frac{1}{x}-y\right)\left(\frac{1}{x}\right)\) From Eq. (i),…
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