The Quotient Rule
Suggested prerequestites:
Definition of the derivative,
The Product Rule
Now that we've seen what a mess products are, we really don't expect
quotients to be very nice either. Once again, we apply the definition
of the derivative in order to find a general formula.
We use the trick of adding zero, this time in the form of
g(x)f(x)-g(x)f(x):
So, the quotient rule for differentiation is "the derivative of the
first times the second minus the first times the derivative of the
second over the second squared." Quite a mouthful but
still useful, trust me.
We can use the quotient rule to find the derivative of
x-n where n is a positive integer, by
writing it instead as
:
Which is what we would would have gotten by applying the power rule. By this, then, we know
that the power rule
can be
applied to all integers.
Exercises:
Find the derivatives of the following functions.
-
-
-
Solutions to the exercises |
Back to the Calculus page |
Back to the World Web Math top page
jjnichol@mit.edu