[m]y`=(\sqrt[3]{x^{5}})`\cdot ctgx+\sqrt[3]{x^{5}}\cdot (ctgx)`=[/m]
[m]=(x^{\frac{5}{3}})`\cdot ctgx+\sqrt[3]{x^{5}}\cdot (ctgx)`=[/m]
[m]=\frac{5}{3}\cdot x^{\frac{5}{3}-1}\cdot ctgx+\sqrt[3]{x^{5}}\cdot (-\frac{1}{sin^2x})=[/m]
[m]=\frac{5}{3}\cdot x^{\frac{2}{3}}\cdot ctgx-\sqrt[3]{x^{5}}\cdot (\frac{1}{sin^2x})=[/m]
[m]=\frac{5}{3} \cdot \sqrt[3]{x^{2}}\cdot ctgx-\sqrt[3]{x^{5}}\cdot (\frac{1}{sin^2x})[/m]
По формуле
[m](\frac{u}{v})`=\frac{u`\cdot v - u\cdot v`}{v^2}[/m]
[m]y`=\frac{(3x^4+cos\frac{x}{3})`\cdot \sqrt{x} - (3x^4+cos\frac{x}{3})\cdot (\sqrt{x})`}{ (\sqrt{x})^2}=[/m]
[m]=\frac{(12x^3+(-sin\frac{x}{3})\cdot (\frac{x}{3})`)\cdot \sqrt{x} - (3x^4+cos\frac{x}{3})\cdot (\frac{1}{2\cdot \sqrt{x}})}{ x}=[/m]
[m]=\frac{24x^4-\frac{2}{3}\cdot x\ sin\frac{x}{3} - 3x^4-cos\frac{x}{3}}{2\cdot x\cdot \sqrt{x}}=[/m]
[m]=\frac{21x^4-\frac{2}{3}\cdot x\ sin\frac{x}{3} -cos\frac{x}{3}}{2\cdot x\cdot \sqrt{x}}[/m]