Найти производную:  1. f(x)=-1/3·x³+4x²+2x   2.φ(x)=4/x²+x∛x    3. g(x)=4ctgx,  g'(-2π/3)   4.h(x)=3x+4/x-3,  h'(4)    

1. [latex]f(x) = -\frac{1}{3}x^3+4x^2+2x[/latex] [latex]f'(x) = -x^2+8x+2[/latex] 2. [latex]f(x) = \frac{4}{x^2}+x\sqrt[3]{x} = \frac{4}{x^2}+x^{\frac{4}{3}}[/latex] [latex]f'(x) = \frac{-2x*4}{x^2}+\frac{4}{3}x^{\frac{4}{3}-1} = -\frac{8}{x}+\frac{4}{3}\sqrt[3]{x}[/latex] 3. g(x) = 4ctgx [latex]g'(x) = -4\frac{1}{sin^2x}[/latex] [latex]g'(-\frac{2\pi}{3}) = -4*\frac{1}{sin^2(-\frac{2\pi}{3})} = -\frac{4}{sin^2(\frac{2\pi}{3})} = -\frac{16}{3}[/latex] 4. h(x) =  3ч+4/(x-3) [latex]h'(x) = 3+ \frac{-4}{(x-3)^2}[/latex]  [latex]h'(4) = 3-\frac{4}{(4-3)^2} = -1[/latex]