COMEDK · Maths · 26. Differentiation
If \(\sqrt{\frac{x}{y}}+\sqrt{\frac{y}{x}}=\sqrt{a}\), then \(y \cdot \frac{d x}{d y}=\)
- A \(\frac{x}{y}\)
- B \(\frac{y}{x}\)
- C \(x\)
- D 0
Answer & Solution
Correct Answer
(C) \(x\)
Step-by-step Solution
Detailed explanation
We have, \[ \begin{array}{r} \sqrt{\frac{x}{y}}+\sqrt{\frac{y}{x}}=\sqrt{a} \\ \left(\sqrt{\frac{x}{y}}+\sqrt{\frac{y}{x}}\right)^{2}=a \\ \frac{x}{y}+\frac{y}{x}+2=a \end{array} \] Differentiating both sides w.r.t. \(x\),…
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