Question

Find dy/dx (derivative) using Implicit Differentiation: xe^y=x-y

Answer 1

[xe^y]' = [x-y]'

x'[e^y] + x[e^y]' = x' - y'

e^y + x[e^y]y' = 1 - y'

y' [xe^y] + y' = 1 - e^y

y' (1 + xe^y) = 1 - e^y

y' = [1 - e^y] / (1 + xe^y)