Page 59 - How To Solve Word Problems In Calculus

Chapter 3

Related Rates

In Chapter 2 we discussed the rate of change of a function.It
is not uncommon for a problem to involve several rates of
change. Related rates problems are concerned with the relation-
ships between several variables and how the rate of change of
one affects the rate of change of another.
In this chapter we consider related rates problems invol-
ving algebraic functions. Problems involving trigonometric
functions are considered in Chapter 6.
The predominant tool used in the solution of related rates
problems is the chain rule. Since most related rates problems
deal with time as the independent variable, we state the chain
rule in terms of t:

dy dy dx
= ·
dt dx dt

Before we discuss how to solve related rates problems, let’s
review some important implications of the chain rule.

EXAMPLE 1
3
Compute the derivative of x with respect to t.

Solution
3
2
The derivative of x with respect to x is 3x . However,
its derivative with respect to t is somewhat different. To
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