AP EAMCET · Maths · Differential Equations
If \(x^y=y^x\), then \(x(x-y \log x) \frac{d y}{d x}\) is equal to :
- A \(y(y-x \log y)\)
- B \(y(y+x \log y)\)
- C \(x(x+y \log x)\)
- D \(x(y-x \log y)\)
Answer & Solution
Correct Answer
(A) \(y(y-x \log y)\)
Step-by-step Solution
Detailed explanation
\(\because x^y=y^x\) Taking log on both sides, we get \(y \log x=x \log y\) On differentiating with respect to \(x\), we get \(y \cdot \frac{1}{x}+\log x \frac{d y}{d x}=x \cdot \frac{1}{y} \frac{d y}{d x}+\log y\)…
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