Question

Для функции z=x^6y^2-3x

найти (z`x-z`y)

в точке M (1;2)

Answer 1

Ответ:

$z = {x}^{6} {y}^{2} - 3x$

$Z'x = 6 {x}^{5} {y}^{2} - 3$

$Z'y = 2 {x}^{6} y$

$Z'x - Z'y = 6 {x}^{5} {y}^{2} - 3 - 2 {x}^{6} y = \\ = 2 {x}^{5} y(3y - x) - 3$

М(1;2)

$Z'x - Z'y = 2 \times 1 \times 2(6 - 1) - 3 = \\ = 4 \times 5 - 3 = 20 - 3 = 17$