A) \[y\text{ }\left[ \frac{1}{2x}+\frac{4}{2x+3}-\frac{1}{2(x+1)} \right]\]
B) \[y\text{ }\left[ \frac{1}{3x}+\frac{4}{2x+3}+\frac{1}{2(x+1)} \right]\]
C) \[y\text{ }\left[ \frac{1}{3x}+\frac{4}{2x+3}+\frac{1}{x+1} \right]\]
D) None of these
Correct Answer: A
Solution :
\[y=\frac{\sqrt{x}{{(2x+3)}^{2}}}{\sqrt{x+1}}\Rightarrow \log y=\frac{1}{2}\log x+2\log (2x+3)-\frac{1}{2}\log (x+1)\] \[\Rightarrow \frac{1}{y}\frac{dy}{dx}=\frac{1}{2x}+\frac{2.2}{(2x+3)}-\frac{1}{2(x+1)}\] or \[\frac{dy}{dx}=y\left[ \frac{1}{2x}+\frac{4}{2x+3}-\frac{1}{2(x+1)} \right]\].
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