Question

Find the dy/dx xy=(x+y)^4

Answer 1

dy/dx = (4 (x + y)^3 - y) / ( x - 4(x + y)^3).

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)