Derivative of ${\cos }^{3}x$ w.r.t. is ${\sin }^{3}x$ is

The derivative of ${\log }_{10}x$ with respect to $x^2$ is

The differential coefficient of ${\log }_{10}x$ with respect to ${\log }_{x}10$ is

If $x=a{\cos }^3\theta , y=a{\sin }^3\theta ,$ then $1+{\left(\frac{dy}{dx}\right)}^2$ is 

If $x=\log \left(1+t^2\right)$ and $y=t-{\tan }^{-1}t,$ then $\frac{dy}{dx}$ is

If $x=a\left(t-\sin t\right)$ and $y=a\left(1-\cos t\right)$, then $\frac{dy}{dx}=$

If $x=2\cos \theta -\cos 2\theta$ and $y=2\sin \theta -\sin 2\theta ,$ then $\frac{dy}{dx}=$

If $\sin x=\frac{2t}{1+t^2}, \tan y=\frac{2t}{1-t^2},$ then $\frac{dy}{dx}$ is equal to