$\lim_{x\to1}\left(\frac{\ln2x^2-1}{\tan\left(x-1\right)}\right)$

$\left(4-8x\right)^{-\frac{1}{2}}$

$\left(3x^2y^2-5x^2y\right)\left(x-xy\right)$

$\frac{d}{dx}3xy+7x^2=2$

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

$\frac{x^3-25x}{x^2+5x}$

$\frac{4x-2}{x+1}$