Summary: 18.024ESG Exam 2
Pramod N. Achar
Spring 2000
1. Let f : R2
R2
and g : R3
R2
be defined by the equations below. Compute the total derivatives
Df, Dg, and D(f g).
f(x, y) = (ex
, x + y)
g(u, v, w) = (uv, uw)
2. The following equation defines z implicitly as a function of x and y. Compute z/x and z/y.
x2
z - xz2
= 2y
1
Answer four of the five parts in questions 36.
3. Decide whether the following statements are true or false.
(a) Let f : R Rn