Z=x+y/x-y частные 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.