A) 1
B) \[\frac{{{x}^{2}}+1}{{{x}^{2}}-4}\]
C) \[\frac{{{x}^{2}}-1}{{{x}^{2}}-4}\]
D) \[{{e}^{x}}\frac{{{x}^{2}}-1}{{{x}^{2}}-4}\]
Correct Answer: C
Solution :
Let\[y=\left[ \log \left\{ {{e}^{x}}{{\left( \frac{x-2}{x+2} \right)}^{3/4}} \right\} \right]=\log {{e}^{x}}+\log {{\left( \frac{x-2}{x+2} \right)}^{3/4}}\]\[\] Þ \[y=x+\frac{3}{4}\,[\log (x-2)-\log (x+2)]\] Þ \[\frac{dy}{dx}=1+\frac{3}{4}\,\left[ \frac{1}{x-2}-\frac{1}{x+2} \right]=1+\frac{3}{({{x}^{2}}-4)}\] Þ \[\frac{dy}{dx}=\frac{{{x}^{2}}-1}{{{x}^{2}}-4}\].You need to login to perform this action.
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