Question

Выполнить дифференцирование функции

Answer 1

Ответ:

${y}^{3} = \frac{x - y}{x + y}$

$3 {y}^{2} \times y'= \frac{(x - y)'(x + y) - (x + y)'(x - y)}{ {(x + y)}^{2} } \\ 3 {y}^{2}y' = \frac{(1 - y')(x + y) - (1 + y')(x - y)}{ {(x + y)}^{2} } \\ 3 {y}^{2} y' {(x + y)}^{2} = x + y - xy' - yy' - x + y - xy'- + yy' \\ 3 {y}^{2} y'{(x + y)}^{2} = 2y - 2xy' \\ 3 {y}^{2} y' {(x + y)}^{2} + 2xy' = 2y \\ y'(3 {y}^{2} (x + y) ^{2} + 2x) = 2y \\ y' = \frac{2y}{3 {y}^{2} {(x + y)}^{2} + 2x }$