AP EAMCET · Maths · Differentiation
If \(\sqrt{x-x y}+\sqrt{y-x y}=1\), then \(\frac{d y}{d x}=\)
- A \(-\sqrt{\frac{y-y^2}{x-x^2}}\)
- B \(-\sqrt{\frac{1-y^2}{1-x^2}}\)
- C \(-\sqrt{\frac{1-y}{1-x}}\)
- D \(-\sqrt{\frac{x-y}{x+y}}\)
Answer & Solution
Correct Answer
(A) \(-\sqrt{\frac{y-y^2}{x-x^2}}\)
Step-by-step Solution
Detailed explanation
\( \sqrt{x(1-y)}+\sqrt{y(1-x)}=1 \) Let \( \sqrt{x}=\sin A \) and \( \sqrt{y}=\sin B \). Then \( \sin A \cos B + \cos A \sin B = 1 \). \( \sin(A+B)=1 \implies A+B = \frac{\pi}{2} \). \( \arcsin(\sqrt{x})+\arcsin(\sqrt{y})=\frac{\pi}{2} \). Differentiate:…
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