$\frac{dy}{dx}=\frac{xy^3}{\sqrt[2]{1+x^2}}$

$\sqrt[2]{x\sqrt[3]{x^2\sqrt[4]{x^3\sqrt[5]{x^4}}}}$

$\int\left(3-2x\right)^{8}dx$

$3xy-6y$

$\lim_{n\to\infty}\left(\frac{\frac{n^4+1}{7n^8+\sqrt[5]{n}}}{\frac{1}{n^{\frac{1}{5}}}}\right)$

$-\:\left(-4\right)\:x\:7\:x\:\left(-1+1\right)$

$\frac{1}{8}\cdot\:\left(3+4\cdot\:\:cos2x+cos4x\right)=cos^4x$