Related Rates: Guidelines and
Examples
Once you have learned implicit differentiation, you can use it to find
a derivative from nearly any equation. In many situations,
each
quantity in the equation changes with time. Any derivative
found
this way is a related
rate. The important thing is that we can see
from the differentiated equation how the rates (derivatives) are
related.
Guidelines for Solving
Related-Rates Problems:
1.
Identify all given quantities
and all quantities to be determined. Make a sketch and label
the
quantities.
2. Write
an equation that uses the variables whose derivatives are either given
or are to be determined.
3. Using
the Chain Rule, implicitly differentiate bothe sides of the equation
with respect to time.
4. After
completing step 3,
substitute into the equation relating the derivatives all known values
for the variables and
their derivatives. Solve for the unknown derivative.
Click on any of the links below to see a related rates problem and
solution.
Ladder
Example 1
Ladder
Example 2
Ladder
Example 3
Piston
Example