Questions in differentiation

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$\frac{d}{{dx}}(\log \tan x) = $
$\frac{d}{{dx}}\log (\log x)$=
$\frac{d}{{dx}}{\left( {\sqrt x + \frac{1}{{\sqrt x }}} \right)^2} = $
If $y = x + \frac{1}{x}$, then
$\frac{d}{{dx}}\left( {\frac{1}{{{x^4}\sec x}}} \right) = $
If $y = 1 + x + \frac{{{x^2}}}{{2\,!}} + \frac{{{x^3}}}{{3\,!}} + ..... + \frac{{{x^n}}}{{n\,!}}$, then $\frac{{dy}}{{dx}} = $
If $y = 1 + x + \frac{{{x^2}}}{{2!}} + \frac{{{x^3}}}{{3!}} + .....\infty ,$then $\frac{{dy}}{{dx}} = $
If $y = \frac{1}{{a - z}},$then $\frac{{dz}}{{dy}} = $
If $y = x\sin x,$ then
$\frac{d}{{dx}}({x^2}{e^x}\sin x) = $

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