$\lim_{x\to a}\left(\frac{8a^3-8x^3}{x-a}\right)$

$\frac{6^{-17}}{6^{-1}}$

$\frac{dy}{dx}=-2y\left(7-y\right)$

$\cot^2x-1=\cos2x\left(1+\cot^2x\right)$

$\frac{d}{dx}\left(tanx^{\frac{1}{x}}\right)$

$\lim_{x\to0}\left(\frac{tan\left(px\right)}{tan\:\left(qx\right)}\right)$

$\frac{dy}{dx}=\frac{x^2}{y^2+1}$