Find the derivatives of the following functions, and point out the increasing, decreasing intervals and minima of the functions according to the positive and negative of the derivatives (1)f(x)=lnx+x; (2)g(x)=x(x+1)(x-3) (3)g(x)=x+2sinx (4)u(x)=5-3x+2x^2-x^3

Find the derivatives of the following functions, and point out the increasing, decreasing intervals and minima of the functions according to the positive and negative of the derivatives (1)f(x)=lnx+x; (2)g(x)=x(x+1)(x-3) (3)g(x)=x+2sinx (4)u(x)=5-3x+2x^2-x^3

(1) F (x) = LNX + X; f '(x) = 1 / x + 1, Let f' (x) = 0 1 / x + 1 = 0 x = - 1, if x > - 1, f '(x) > 0, if x0, if (2 - √ 13) / 30, if x = (2 - √ 13) / 3, if f' (x) = x = (2 + √ 13) / 3, if f (x) = (3) g (x) = x + 2S