If $xy = c^2$ where $c$ is a constant,then $\frac{dy}{dx}$ is equal to

$A$ particular straight line passes through the origin and a point whose abscissa is double the ordinate of the point. The equation of such a straight line is:

As $\theta$ increases from $0^{\circ}$ to $90^{\circ}$,the value of $\cos \theta$ :-

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( \frac{1}{x^4 \sec x} \right) = $

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