$\lim_{x\to o}\left(1+\sin\left(4x\right)^{\cot\left(x\right)}\right)$

$\left(4m^5n-m^2n^4\right)^4$

$\frac{\sqrt{-16x^3}}{-8x^{-2}}$

$10m^2-5m^4+15m^3$

$\frac{dy}{dx}\left(y=arctan\left(\frac{x}{2}\right)+arctan\left(\frac{2}{x}\right)\right)$

$\sqrt{5a^3}$

$3x^2\left(x^3+3\right)^3$