Find the derivative if x^3 + 4xy^2 - y^4 = 7

Answer 1

x^3 + 4xy^2 - y^4 = 7 --->

d[x^3 + 4xy^2 - y^4 ] = 0 ----->

3x^2 dx + 4y^2 dx + 8yx dy -4 y^3 dy = 0

3x^2 dx + 4y^2 dx =(4y^3 - 8yx) dy -->

3x^2+ 4y^2=(4y^3 - 8yx) dy/dx ---->

dy/dx = (3x^2+ 4y^2)/(4y^3 - 8yx)