MCQ
${d \over {dx}}\left[ {\log \left\{ {{e^x}{{\left( {{{x - 2} \over {x + 2}}} \right)}^{3/4}}} \right\}} \right]$ is equals to
- A$1$
- B${{{x^2} + 1} \over {{x^2} - 4}}$
- ✓${{{x^2} - 1} \over {{x^2} - 4}}$
- D${e^x}{{{x^2} - 1} \over {{x^2} - 4}}$
$= \log {e^x} + \log {\left( {\frac{{x - 2}}{{x + 2}}} \right)^{3/4}}$
==> $y = x + \frac{3}{4}\,[\log (x - 2) - \log (x + 2)]$
==> $\frac{{dy}}{{dx}} = 1 + \frac{3}{4}\,\left[ {\frac{1}{{x - 2}} - \frac{1}{{x + 2}}} \right] $
$= 1 + \frac{3}{{({x^2} - 4)}}$
==> $\frac{{dy}}{{dx}} = \frac{{{x^2} - 1}}{{{x^2} - 4}}$.
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$STATEMENT -1$ : The function $F(x)$ satisfies $F(x+\pi)=F(x)$ for all real $x$. because
$STATEMENT -2$$: \sin ^2(x+\pi)=\sin ^2 x$ for all real $x$.