Answer:
dy/dx = (4 (x + y)^3 - y) / ( x - 4(x + y)^3).
Step-by-step explanation:
xy = (x + y)^4
Using implicit differentiation:
x dy/dx + y*1 = 4 (x + y)^3 * (1 + dy/dx)
x dy/dx + y = 4 (x + y)^3 + 4 dy/dx (x + y)^3
x dy/dx - 4 dy/dx (x + y)^3 = 4 (x + y)^3 - y
dy/dx( x - 4(x + y)^3) = 4 (x + y)^3 - y
dy/dx = (4 (x + y)^3 - y) / ( x - 4(x + y)^3)
