$\lim_{x\to\:0}\frac{\left(6-6^{e^{x^2+y^2}}\right)}{3x^2+3y^2}$

$\frac{4a^4b}{5\:}-\frac{4ab^4}{5}$

$7x+12=10x$

$\frac{d}{dx}\left(xy+\sin\left(xy\right)=0\right)$

$\frac{d}{dx}e^x\sqrt{x}$

$\frac{\left(x+8\right)}{x}=\frac{63}{x-8}$

$\lim_{x\to5}\left(\frac{x-5}{\sqrt{x-3}-\sqrt{2}}\right)$