TS EAMCET · Maths · Differentiation
If \(u(x, y)=y \log x+x \log y\), then \(u_x u_y-u_x \log x-u_y \log y+\log x \log y\) is equal to :
- A 0
- B -1
- C 1
- D 2
Answer & Solution
Correct Answer
(C) 1
Step-by-step Solution
Detailed explanation
We have, \(u(x, y)=y \log x+x \log y\) On differentiating partially w.r.t. \(x\) and \(y\) respectively, \(u_x=\frac{y}{x}+\log y, u_y=\log x+\frac{x}{y}\) Now, \(u_x u_y-u_x \log x-u_y \log y+\log x \log y\)…
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