Question

Compute fx and fy for the following functions and evaluate them at the indicated points.

(a) f (x, y) = x y + x − y; (1, 1)

(b) f (x, y) = x/y; (1, 1)

Answer 1

(a) We have

fx (x, y) = y + 1

fy (x, y) = x − 1 ,

and so fx (1, 1) = 2 and f y (1, 1) = 0.

(b) We have

(c) We have

(d) We have

(f) To compute the y-derivative we write f (x, y) = x y = e y ln x . We have