Question

Calcular la derivada implícita dy/dx: 7x^3 y^2+5y^2+3x=x^2+y

Answer 1

d /d x  ( 7 x ^3 y^ 2 + 5 y ^2 + 3 x )  =  d /d x  ( x ^2 + y )

d/dx [7x^3y^2] + d/dx [5y^2] + d/dx [3x]

Evalue d/dx [7x^3y^2]

7 (2x^3y d/dx [y]+3y^2x^2) + d/dx [5y^2] + d/dx [3x]

evalue d/dx [5y^2]

7 (2x^3y d/dx [y]+3y^2x^2) + 10y d/dx [y] + d/dx [3x]

Evalue d/dx [3x]

7 (2x^3y d/dx [y]+3y^2x^2) + 10y d/dx [y] + 3x

simplifica

14x^3y d/dx [y] + 21x^2y^2 + 10y d/dx [y]+ 3

2x + d/x [y]

14x^3 yy' + 21x^2y^2 + 10yy' + 3 =2x + y'

y'= - 21x^2y^2 - 2x + 3/ 14x^3y + 10y -1

remplace y' con dy/dx = 21x ^2y^2 - 2x + 3/ 14x^3y + 10y -1