1. 31 – Power, Product, Quotient Rule No Calculator
Derivative Investigations
31 – Power, Product, Quotient Rule No Calculator

2. The derivative of f(x) with respect to x is the function f ‘ (x) [read “f prime of x”]:
Symbols for the derivative with respect to x
Differentiation – the process of computing derivatives

3. Methods of Differentiation
The computing of
results in ‘patterns’ of answers.
Knowing these patterns (which will require memorization) can shorten the work necessary compute:
Below are four functions and the answer to
Discuss and see if you can find the pattern.

4. Based upon the pattern you saw, given the two functions below, find f ‘ (x).
Our first ‘method of differentiation’: The Polynomial Rule of Differentiation

5. Given f(x), find f ‘ (x).
Rewrite g(x) as a polynomial. Then find g ‘ (x).

6. The Product Rule of DifferentiationOR
where
F represents a function (first factor)
S represents a function (second factor)

7. Product Rule Examples
Try one…..

8. Given y below, find
You need NOT simplify your answer.

9. The Quotient Rule of DifferentiationOR

10. Quotient Rule Examples

11. Given y below, find
You need NOT simplify your answer.

13. The derivative of a derivative is referred to as the ‘second derivative’.