$\lim_{x\to\infty}\left(\frac{1-\cos\left(5x\right)}{10x}\right)$

$\frac{x^3+2x+3}{x^2+1}$

$\lim_{x\to\infty}\left(5x+\frac{4}{x}\right)$

$\frac{24x^3+10x^2-62x+15}{4x-5}$

$\frac{dy}{dx}\left(\sqrt{x+1}=4\right)$

$2a+3b+5a-5b$

$\frac{d}{dx}\left(tan^{-1}\left(3x^2y\right)=x+4xy^2\right)$