A) \[\frac{{{x}^{2}}-7}{{{x}^{2}}-4}\]
B) 1
C) \[\frac{{{x}^{2}}+1}{{{x}^{2}}-4}\]
D) \[{{e}^{x}}\frac{{{x}^{2}}-1}{{{x}^{2}}-4}\]
Correct Answer: A
Solution :
\[y=\log {{e}^{x}}+\frac{3}{4}\log \frac{x+2}{x-2}=x+\frac{3}{4}\log \frac{x+2}{x-2}\] Þ \[y=x+\frac{3}{4}\left[ \log (x+2)-\log (x-2) \right]\] \[\frac{dy}{dx}=1+\frac{3}{4}\left[ \frac{1}{x+2}-\frac{1}{x-2} \right]=1-\frac{3}{{{x}^{2}}-4}\] \[\frac{dy}{dx}=\frac{{{x}^{2}}-7}{{{x}^{2}}-4}\].
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