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

$\lim_{x\to3}\left(\frac{x^4+x^3-27x-27}{x^3+2x^2-4x-18}\right)$

$\left(x+4y\right)^2-\left(3x-2\right)\left(3x+2\right)$

$\left[2x-\left(3-b\right)\right]\left[2x+\left(3-b\right)\right]$

$\lim_{x\to1.01}\left(\frac{4x^2-x-3}{x-1}\right)$

$\frac{dy}{dx}=\frac{3x-2y}{3x-2y+1}$

$\int\frac{6x^3}{\left(\sqrt{x^2+9}\right)}dx$