31 – Power, Product, Quotient Rule No Calculator

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Presentation transcript:

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

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

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.

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

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

The Product Rule of Differentiation OR where F represents a function (first factor) S represents a function (second factor)

Product Rule Examples Try one…..

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

The Quotient Rule of Differentiation OR

Quotient Rule Examples

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

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