$\frac{d}{dx}(\sin(x^2) + \cos(x^2)) = $ . . . . . .

The derivative of $\sqrt{\sqrt{x} + 1}$ is

The solution set of $f'(x) > g'(x)$,where $f(x) = \frac{1}{2} (5^{2x+1})$ and $g(x) = 5^x + 4x \ln 5$ is:

$A$ particle starts from rest and its angular displacement (in radians) is given by $\theta = \frac{t^{2}}{20} + \frac{t}{5}$. If the angular velocity at the end of $t = 4 \ s$ is $k$,then the value of $5k$ is

If $y = \cos^{-1}(\tanh x) + \sinh(\sin 6x)$,then $\frac{dy}{dx} =$

If $f(x)=x^{n}$,where $n$ is a non-negative integer,then the values of $n$ for which $f^{\prime}(\alpha+\beta)=f^{\prime}(\alpha)+f^{\prime}(\beta)$ for all $\alpha, \beta > 0$ is: