Question

Find f' if x power 7 + y power 7 = 8xy

Answer 1

x^7 + y^7 = 8xy

7x^6 dx+7y^6 dy=8y dx + 8x dy

dy(7y^6-8x)=dx(8y-7x^6)

solve for dy/dx

Answer 2

x^7 + y^7 = 8xy
7x^6 + 7y^6 y' = 8y + 8x y'
8x y' - 7y^6 y' = 7x^6 - 8y
y'(8x - 7y^6) = 7x^6 - 8y
y' = (7x^6 - 8y)/(8x - 7y^6)