Name:______________________________
Vector Calculus Exam 2 October 18th
There are 7 problems and 144 points total. The point value of each question is indicated. Read each
question carefully!
1. (24 points.) Let 23 3),( xyxyxf += and yxyyxg 23 3),( += Compute the following
a.
()
=+
∂
∂),(),( yxgyxf
x
b.
()
=−
∂
∂),(),( yxgyxf
y
c. (2 ( , ))fxy∇=
2. Use the figure below to answer the following questions
a) (3 points) What is the sign of the derivative at point A in the direction of the vector shown at A?
b) (3 points) What is the sign of the derivative at point B in the direction of the vector shown at B?
c) (6 points) Draw a vector in the direction of the gradient at point A
d) (6 points) Draw a vector in the direction of the gradient at point B.
