TS EAMCET · Maths · Differentiation
If \(u=\sin ^{-1}\left(\frac{x}{y}\right)+\tan ^{-1}\left(\frac{y}{x}\right)\), then the value \(x \frac{\partial u}{\partial x}+y \frac{\partial u}{\partial y}\) is
- A 0
- B 1
- C 2
- D None of these
Answer & Solution
Correct Answer
(A) 0
Step-by-step Solution
Detailed explanation
Let \(u(x,y)=\sin ^{-1}\left(\frac{x}{y}\right)+\tan ^{-1}\left(\frac{y}{x}\right)\). Substitute \(x \to tx\) and \(y \to ty\): \(u(tx,ty) = \sin ^{-1}\left(\frac{tx}{ty}\right)+\tan ^{-1}\left(\frac{ty}{tx}\right)\)…
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