Spring 2006

Show all work in a neat and organized fashion. Clearly indicate your answers.

20 points possible.

1. (4 pts.) Differentiate.

g(t)=t5cost

2. (4 pts.) Find the derivative.

y=sec3 x+tan5 x

3. (4 pts.) Suppose f and g are the functions whose graphs are shown on the supplemental page. Let u(x)=f(g(x)). Find u¢(3), if it exists. If it does not exist, explain why.

4. (4 pts.) Find

dy dx .

x3+x2y+4y2=6

5. (4 pts.) Find

d2y dx2 .

y=(x5+1)2/3