Find equation of normal line to the graph of the equation

Question

e^(x+y)=xy+5 at (2,-2)

Answer 1

Implicitly differentiate: e^{x + y}(1 + y') = y + xy'. At point (2, - 2) we have e⁰(1 + y') = - 2 + 2y'; y' = 3.

Slope m of normal line: m = - 1/y' = - 1/3; y + 2 = - 1/3(x - 2); y = - 1/3x - 4/3.