Product Rule Practice
Derivative rules we learned thus far:
Let
and
, then the derivative of the product of these two functions is:
Note: The derivative of a product of two functions is
the product of the derivative of each function.
Now, we want to focus on the product of two (or more functions). That is, if
are differentiable functions, then
and
Alternatively, we sometimes see this written as: (uv)' =
The derivative of a product of two functions is
the derivative of the first function
For a quick demonstration,
these two functions is:
and
Product Quotient Rule Page 1
PLUS the
derivative of the second function.
, then the derivative of the product of
Product Rule Practice
Consider each of the following:
(A)
find
.
(B)
(C)
, find g'(t)
note:
find h'(x)
Extension, what is the derivative of
Generalization, the derivative of
Where do the horizontal tangents occur for
? (Use our knowledge of calculus)
Product Quotient Rule Page 2
Product Rule Practice
If
and
are differentiable, then a further extension to the product rule:
Find the derivative of
Product Quotient Rule Page 3
Quotient Rule Practice
Now, we want to focus on the Quotient of two functions. That is, if
functions, then
Example: Let
Example: Let
, find
.
, find h' (x).
Product Quotient Rule Page 4
and
are differentiable
Last Example
Consider the curve given by
(a) Using knowledge of calculus determine where the horizontal tangents occur?
(b) Find the equation of the tangent line to the curve at x = 2.
Product Quotient Rule Page 5