Решите уравнение:   1. f'(x)·g'(x)=0     f(x)=x³-3x²     g(x)=2/3√x   2. f(x)=(1+2x)(2x-1)     f'(-2)   3.φ(x)=3+x/√x    φ'(8)   4. g(x)=4sinx     g'(-π/3) 

1) f'(x)*g'(x) = 0 [latex]f'(x) = 3x^2-6x[/latex]  [latex]g'(x) = -\frac{1}{3\sqrt{x^3}}[/latex]  [latex](3x^2-6x)(-\frac{1}{3}\frac{1}{\sqrt{x^3}})=0[/latex]  [latex]\frac{6x-3x^2}{3x^{\frac{3}{2}}}=0[/latex]  [latex]\frac{3x(2-x)}{3x\sqrt{x}} =0 [/latex]  [latex]x\neq0[/latex]  x = 2  2) [latex]f(x) = (1+2x)(2x-1) = 4x^2-1[/latex] [latex]f'(x) = 8x[/latex]  [latex]f'(-2) = -16[/latex]  3) [latex]f(x) = 3 + \frac{x}{\sqrt{x}} = 3+\sqrt{x}[/latex] [latex]f'(x) = -\frac{1}{2\sqrt{x}}[/latex]  [latex]f'(8) = -\frac{1}{2\sqrt{8}}=-\frac{1}{4\sqrt{2}}[/latex]  4) g(x) = 4sinx g'(x) = 4cosx [latex]g'(-\frac{\pi}{3}) = 4cos(-\frac{\pi}{3}) = 4*\frac{1}{2} = 2[/latex]