Solve frac{(+sqrt[3]{3n^{2}-n^{3}})(n-3sqrt{3n^2-n^3})}{n-sqrt[3]{3n^2n^3}}

$$\frac { ( + \sqrt[ 3 ] { 3 n ^ { 2 } - n ^ { 3 } } ) ( n - 3 \sqrt { 3 n ^ { 2 } - n ^ { 3 } } ) } { n - \sqrt[ 3 ] { 3 n ^ { 2 } n ^ { 3 } } }$$

Evaluate

$$\frac{\sqrt[3]{\frac{3-n}{n}}\left(-3\sqrt{3-n}|n|+n\right)}{-\sqrt[3]{3}n^{\frac{2}{3}}+1}$$

Differentiate w.r.t. n

$$\frac{-18\sqrt[3]{3}\sqrt{3-n}sign(n)n^{\frac{8}{3}}-18nsign(n)\left(3-n\right)^{\frac{3}{2}}+54\sqrt[3]{3}\sqrt{3-n}sign(n)n^{\frac{5}{3}}+3^{\frac{4}{3}}\sqrt{3-n}|n|n^{\frac{5}{3}}+2\sqrt[3]{3}n^{\frac{8}{3}}+9\sqrt{3-n}n|n|-54\sqrt[3]{3}\sqrt{3-n}n^{\frac{2}{3}}|n|-6n^{2}+6\times 3^{\frac{4}{3}}n^{\frac{5}{3}}-18\sqrt[3]{3}n^{\frac{5}{3}}+18\sqrt{3-n}|n|+12n}{6\left(3-n\right)^{\frac{2}{3}}n^{\frac{4}{3}}\left(-\sqrt[3]{3}n^{\frac{2}{3}}+1\right)^{2}}$$