Question

Derivada implícita de (2-3x)^2-xy=y^3+4yx^2

Answer 1

${(2 - 3x)}^{2} - xy = {y}^{3} + 4y {x}^{2} \\ derivada \: implicit \: iguaal \: a.... \\ 2(2 - 3x)( - 3) - (y + x( {y}^{1} )) = 3 {y}^{2} ( {y}^{1} ) + 8xy + 4 {x}^{2} ( {y}^{1} ) \\ - 12 + 18x - y - 8xy= 3 {y}^{2} ({y}^{1} ) + 4 {x}^{2} ( {y}^{1} ) + x( {y}^{1} ) \\ 18x - 8xy - y - 12 = ( {y}^{1} )(3 {y}^{2} + 4 {x}^{2} + x) \\ \frac{18x - 8xy - y - 12}{3 {y}^{2} + 4 {x }^{2} + x } = {y}^{1}$
y^1=derivada implicita
saludos......