A) \[\frac{\sqrt{x}}{1-x}\]
B) \[\frac{1}{\sqrt{x}(1-x)}\]
C) \[\frac{\sqrt{x}}{1+x}\]
D) \[\frac{1}{\sqrt{x}(1+x)}\]
Correct Answer: B
Solution :
\[t=\frac{5x+1}{10{{x}^{2}}-3},\] Differentiating w.r.t. x of y, we get \[\frac{dy}{dx}=\frac{1-\sqrt{x}}{1+\sqrt{x}}\left[ \frac{(1-\sqrt{x})\frac{1}{2\sqrt{x}}+(1+\sqrt{x})\frac{1}{2\sqrt{x}}}{{{(1-\sqrt{x})}^{2}}} \right]\] \[=\frac{1}{2(1-x)\sqrt{x}}[1-\sqrt{x}+1+\sqrt{x}]=\frac{1}{\sqrt{x}(1-x)}\].
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