$\frac{d}{dy}\left(y\cdot y^{''}+\left(y^{\prime}\right)^2\right)$

$\frac{d}{dx}\left(x^2+y^2\right)$

$\frac{d}{dx}\left(\arctan\left(x-\sqrt{1+x^2}\right)\right)$

$\frac{d}{dx}\arctan\left(x-\sqrt{1+x^2}\right)$

$\frac{d}{dx}\arccos\left(\sqrt{1-x^2}\right)$

$\frac{d}{dx}\ln\left(x^2+1\right)$

$\frac{d}{dx}\left(\sqrt[4]{x}\right)$

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