805 Найти производную функции:
1) x^2+1/x^3
2) x^3 + 1/x^2
3) 2∜x - √x
4) ...
1) [m]x^2+\frac{1}{x^3})`=(x^2)+(x^{-3})`=2x-3x^{-4}=2x-\frac{3}{x^4}[/m]
2) [m]x^3+\frac{1}{x^2})`=(x^3)+(x^{-2})`=3x^2-2x^{-3}=3x^2-\frac{2}{x^3}[/m]
3) [m]2\sqrt[4]{x}-\sqrt{x})`=2(x^{\frac{1}{4}})`-(x^{\frac{1}{2}})`=2\cdot \frac{1}{4}\cdot x^{\frac{1}{4}-1}-\frac{1}{2}\cdot x^{\frac{1}{2}-1}=\frac{1}{2}\cdot x^{-\frac{3}{4}}-\frac{1}{2}\cdot x^{-\frac{1}{2}}=\frac{1}{2\sqrt[4]{x^3}}-\frac{1}{2\sqrt{x}}[/m]
4)[m]3\sqrt[6]{x}+7\sqrt[14]{x})`=3(x^{\frac{1}{6}})`+7(x^{\frac{1}{14}})`=3\cdot \frac{1}{6}\cdot x^{\frac{1}{6}-1}+7\cdot \frac{1}{14}\cdot x^{\frac{1}{14}-1}=\frac{1}{2}\cdot x^{-\frac{5}{6}}+\frac{1}{2}\cdot x^{-\frac{13}{14}}=\frac{1}{2\sqrt[6]{x^5}}-\frac{1}{2\sqrt[14]{x^{13}}}[/m]
804.