TS EAMCET · Maths · Differentiation
If \(x \sqrt{1+y}+y \sqrt{1+x}=0\), then \(\frac{d y}{d x}=\)
- A \(\frac{-1}{(1+x)^2}\)
- B \(\frac{1}{(1+x)^2}\)
- C \(\frac{2}{(1+x)^{3 / 2}}\)
- D \(\frac{-2}{(1+x)^{1 / 2}}\)
Answer & Solution
Correct Answer
(A) \(\frac{-1}{(1+x)^2}\)
Step-by-step Solution
Detailed explanation
Given, \(x \sqrt{1+y}+y \sqrt{1+x}=0\) \(\Rightarrow \quad x^2(1+y)=y^2(1+x) \Rightarrow x^2-y^2=x y(y-x)\) \(\Rightarrow \quad x+y+x y=0 \Rightarrow y=\frac{-x}{1+x}\) On differentiating w.r.t ' \(x\) ', we get…
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