Find the derivative $\frac{d}{dx}\left(\mathrm{arccot}\left(x\right)+\mathrm{arccot}\left(\frac{1}{x}\right)\right)$ using the sum rule

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

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

$\frac{d}{dx}\left(\sqrt{\frac{x\left(x+2\right)}{\left(2x+1\right)\left(5x+3\right)}}\right)$

Find the derivative

$\frac{d}{dx}\left(\frac{\left(x^3+1\right)^4sin^2x}{x^{\frac{1}{3}}}\right)$

Find the derivative

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

Find the derivative

$\frac{d}{dx}\left(\frac{2x^3}{\left(2-5x\right)\sqrt{x^2+1}}\right)$

Find the derivative

$\frac{d}{dt}\left(\frac{\sqrt{t-4}}{tcos\left(t\right)}\right)$