$\frac{d}{d x}\left(e^{\log _e \sqrt{1+\tan ^2 x}}\right) =$

If $f(x) = \sum_{p=1}^7 p^2 \sin^{-1}\left(\frac{4}{5} \sin(px) - \frac{3}{5} \cos(px)\right)$,then the value of $\frac{df}{dx}$ at $x = 1$ is (Given that $\sin^{-1}(\sin x) = x$)

The differential coefficient of $\log _{10} x$ with respect to $\log _{x} 10$ is

If $y = \frac{a + b{x^{3/2}}}{{x^{5/4}}}$ and $y' = 0$ at $x = 5$,then the ratio $a:b$ is equal to

If $h(x) = \sqrt{4f(x) + 3g(x)}$,$f(1) = 4$,$g(1) = 3$,$f'(1) = 4$,and $g'(1) = 3$,then find $h'(1)$.

If $r = [2\phi + \cos^2(2\phi + \pi/4)]^{1/2}$,then what is the value of the derivative $dr/d\phi$ at $\phi = \pi/4$?