Z=x+y/x-y приватные производные

y = (((x - 1)^3) * x^(-2)) = ((x - 1)^3) * x^(-2) + ((x - 1)^3) * (x^(-2)) = (3(x - 1)^2) * x^(-2) + ((x - 1)^3) * (-2x^(-3)) = (3(x - 1)^2) / x^2 + ((x - 1)^3) / (-2x^3).

y = ((3(x - 1)^2) / x^2 + ((x - 1)^3) / (-2x^3)) = ((3(x - 1)^2) * x^(-2) + ((x - 1)^3) * (-2x^(-3))):

1) (3(x - 1)^2) = 3 * (x - 1) * ((x - 1)^2) = 3 * ((x) (1)) * ((x - 1)^2) = 3 * (1 * x^(1 1) 0) * (2 * (x - 1)^(2 - 1)) = 6(x - 1);

2) (x^(-2)) = (-2) * x^(-2 1) = (-2) * x^(-3) = -2x^(-3);

3) ((x - 1)^3) = ((x - 1)^3) = (x - 1) * ((x - 1)^3) = ((x) (1)) * ((x - 1)^3) = (1 * x^(1 1) 0) * (3 * (x - 1)^(3 - 1)) = 3(x - 1)^2;

4) (-2x^(-3)) = (-2) * (-3) * x^(-3 1) = 6 * x^(-4) = 6x^(-4).

y = ((3(x - 1)^2) * x^(-2)) + (((x - 1)^3) * (-2x^(-3))) = (((3(x - 1)^2) * x^(-2) + ((3(x - 1)^2) * (x^(-2))) + (((x - 1)^3) * (-2x^(-3)) + ((x - 1)^3) * (-2x^(-3))) = (6(x - 1) * x^(-2) + ((3(x - 1)^2) *( -2x^(-3))) + (((3(x - 1)^2) * (-2x^(-3)) + ((x - 1)^3) * (6x^(-4))) = 6(x - 1) * x^(-2) + ((3(x - 1)^2) *( -2x^(-3)) + ((3(x - 1)^2) * (-2x^(-3)) + ((x - 1)^3) * (6x^(-4)) = 6(x - 1) * x^(-2) + ((6(x - 1)^2) *( -2x^(-3)) + ((x - 1)^3) * (6x^(-4)) = 6(x - 1) / x^2 - 12(x - 1)^2) / x^3 + 6(x - 1)^3 / x^4.