Question

50 баллов. найти производную функции

Answer 1

Ответ:

${x}^{4} + {y}^{4} = {x}^{2} {y}^{2} \\ 4 {x}^{3} + 4 {y}^{3} \times y' = ( {x}^{2} )' {y}^{2} + ( {y}^{2} ) '{x}^{2} \\ 4 {x}^{3} + 4 {y}^{3} y' = 2x {y}^{2} + 2yy' {x}^{2} \\ 4 {y}^{3} y' - 2yy' {x}^{2} = 2x {y}^{2} - 4 {x}^{3} \\ y'(4 {y}^{3} - 2y {x}^{2} ) = 2x {y}^{2} - 4 {x}^{3} \\ y' = \frac{2x {y}^{2} - 4 {x}^{3} }{4 {y}^{3} - 2 {x}^{2}y } \\ y' = \frac{x {y}^{2} - 2 {x}^{3} }{2 {y}^{3} - {x}^{2}y }$