1)
[m]F`(x)=(5x+\frac{7}{x})`=(5x)`+(\frac{7}{x})`=5+(7\cdot (x^{-1})`=5+7\cdot (-1)\cdot x^{-1-1}==5-\frac{7}{x^2}=f(x)[/m]
[m]F`(x)=f(x)[/m]
2)
[m]F`(x)=(9- ctg \frac{x}{3})`=(9)`-(ctg\frac{x}{3})`=0-(-\frac{1}{sin^2\frac{x}{3}})\cdot (\frac{x}{3})`=\frac{1}{sin^2\frac{x}{3}}\cdot \frac{1}{3}=\frac{1}{3sin^2\frac{x}{3}}=f(x)[/m]
[m]F`(x)=f(x)[/m]
[b]2.[/b]
1)
см. приложение1
[m]F(x)=12\cdot \frac{x^{2+1}}{2+1}-6\cdot \frac{x^{5+1}}{5+1}[/m]
[m]F(x)=12\cdot \frac{x^3}{3}-6\cdot \frac{x^{6}}{6}[/m]
[m]F(x)=4x^3-x^{6}[/m]
2)
см. приложение 2
[m]F(x)=7\cdot tgx+2\cdot (-cosx)[/m]
[m]F(x)=7\cdot tgx-2cdot cosx[/m]
3)
[m]f(x)=x^{\frac{3}{4}}-9\cdot x^{-\frac{1}{4}}[/m]
см. приложение 1
[m]F(x)= \frac{x^{\frac{3}{4}+1}}{\frac{3}{4}+1}-9\cdot \frac{x^{-\frac{1}{4}+1}}{-\frac{1}{4}+1}[/m]
[m]F(x)= \frac{x^{\frac{7}{4}}}{\frac{7}{4}}-9\cdot \frac{x^{\frac{3}{4}}}{\frac{3}{4}}[/m]
[m]F(x)= \frac{4}{7}\cdot \sqrt[4]{x^7}-9\cdot \frac{4}{3}\cdot \sqrt[4]{x^3}[/m]
[m]F(x)=\frac{4}{7}\cdot x\cdot \sqrt[4]{x^3}-12\cdot \sqrt[4]{x^3}[/m]