If $G(x) = -\sqrt{25-x^{2}}$,then $\lim _{x \rightarrow 1} \frac{G(x)-G(1)}{x-1}$ is

$\frac{d}{dx}(\sin 2x^2)$ equals

$A$ 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 $y = \sqrt{\sin \sqrt{x}}$,then $\frac{dy}{dx} = $

Given that $\frac{d}{dx}f(x) = f'(x)$. The relationship $f'(a + b) = f'(a) + f'(b)$ is valid if $f(x)$ is equal to

If $y = (1 + x^{1/4})(1 + x^{1/2})(1 - x^{1/4})$,then $\frac{dy}{dx} = $