The function $f(x)=e^x+x$ being differentiable and one to one, has a differentiable inverse $f^{-1}(x)$, then find $\dfrac {d}{dx} (f^{-1}(x))$ at the point $f(log_e 2)$.

$\frac{d}{d x}\left(\frac{\sqrt{1+\sin 2 x}}{\sin x+\cos x}\right)=?$

x এর মান কত হলে $\mathrm{\frac{x}{lnx}}$ এর মান ক্ষুদ্রতম হবে?

If $f(x) = \frac{{{e ^{4x}}}}{{1 + 2{e ^x}}} than\,\,f'\left( 0 \right)\,\,is-$

If $y=e^{\sin^{2}x +\sin^{4}x + \sin ^{6}x +....+\infty}$ , then $\dfrac {dy}{dx} =?$