 
Summary: Math 1550 Fall 2005
Section 31 P. Achar
Exam 3 Solutions
October 27, 2005
Total points: 50 Time limit: 1 hour
No calculators, books, notes, or other aids are permitted. You must show your work and justify your
steps to receive full credit.
1. (5 points) Short answer:
(a) Suppose h(x) = f(g(x)). Given the following information, find h (3).
f(2) = 1 f(3) = 4 g(3) = 2 g(4) = 3
f (2) = 7 f (3) = 3 g (3) = 5 g (4) = 1
h (3) =
Solution: The chain rule says h (x) = f (g(x))g (x), so
h (3) = f (g(3))g (3) = f (2)f (3) = 7 · 5 = 35.
(b) What is the point of logarithmic differentiation? (In other words, what can one do with logarithmic
differentiation that one can't do otherwise?)
Solution: Functions of the form f(x)g(x)
(like (sin x)x
) don't fit any of the differentiation rules
that we have. To find the derivative of such a function, we must use logarithmic differentiation.
