The value of $\frac{d}{dx} (\cos 4x^2)$ is .......

If $\angle P - \angle Q = 50^{\circ}$,then find the values of $\angle P$ and $\angle Q$.

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

The slope of the graph as shown in the figure at points $1, 2$ and $3$ is $m_1, m_2$ and $m_3$ respectively. Then:

What is the value of $\alpha$ if $\alpha = \frac{25}{50}$?

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