If $\tan \theta = \frac{1}{\sqrt{5}}$ and $\theta$ lies in the first quadrant,the value of $\cos \theta$ is:

If $x^3+3xy+y^3=1$,then the correct option$(s)$ is/are:-
$(A) \left(\frac{dy}{dx}\right)_{(1,1)}=-1$
$(B) \left(\frac{dy}{dx}\right)_{(1,1)}=-2$
$(C) \left(\frac{dy}{dx}\right)_{(1,0)}=-1$
$(D) \left(\frac{dy}{dx}\right)_{(1,0)}=-3$

$\frac{d}{dx} {\left( \sqrt{x} + \frac{1}{\sqrt{x}} \right)}^2$ is equal to

The greatest value of the function $-5\, \sin\, \theta + 12\, \cos\, \theta$ is

If $y = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + .....\infty$,then $\frac{dy}{dx} = $

The value of $\frac{d}{dx}(\log_e x)$ is: