[m]y`=(x)`\cdot sinx+x\cdot (sinx)`=1\cdot sinx+x\cdot cosx=sinx+x\cdot cosx;[/m]
7)правило: (u*v)`=u`*v+u*v`
[m]y`=(\sqrt{x})`\cdot cos+\sqrt{x}\cdot (cosx)`=\frac{1}{2\sqrt{x}}\cdot cosx+\sqrt{x}\cdot (-sinx)=[/m]
=[m]\frac{cosx}{2\sqrt{x}}-\sqrt{x}\cdot sinx[/m]
8) правило: [m](\frac{u}{v})`=\frac{u`v-uv`}{v^2}[/m]
[m]y`=(\frac{x^2}{x^2+1})`=\frac{(x^2)`\cdot (x^2+1)-x^2\cdot (x^2+1)`}{(x^2+1)^2}=[/m]
[m]=\frac{2x\cdot (x^2+1)-x^2\cdot 2x}{(x^2+1)^2}=\frac{2x^3+2x-2x^3}{(x^2+1)^2}=[/m]
[m]=\frac{2x}{(x^2+1)^2}[/m]
9)правило: [m](\frac{u}{v})`=\frac{u`v-uv`}{v^2}[/m]
[m]y`=(\frac{3\sqrt{x}}{2x+9})`=\frac{(3\sqrt{x})`\cdot (2x+9)-3\sqrt{x}\cdot (2x+9)`}{(2x+9)^2}=[/m]
[m]=\frac{\frac{3}{2\sqrt{x}}\cdot (2x+9)-3\sqrt{x}\cdot 2}{(2x+9)^2}=[/m]
[m]=\frac{6x+27-12x}{2\sqrt{x}(2x+9)^2}=\frac{27-6x}{2\sqrt{x}(2x+9)^2}[/m]
10)правило: [m](\frac{u}{v})`=\frac{u`v-uv`}{v^2}[/m]
[m](\frac{sinx}{x})`=\frac{(sinx)`\cdot x-sinx\cdot (x)`}{(x)^2}=[/m]
[m]=\frac{cosx \cdot x-sinx\cdot 1}{x^2}=[/m]
[m]=\frac{x\cdot cosx-sinx}{x^2}[/m]