1. The Product Rule for Differentiation

2. If you had to differentiate f(x) = (3x + 2)(x – 1), how would you start?

3. Examine the original function f(x) = (3x + 2)(x – 1) It is a product of two functions. What are they? g(x) = and h(x) = Since f(x) = g(x) h(x) does f / (x)  g / (x) h / (x) ?

4. We can derive this function another way as shown below. Where do the parts come from? When we expanded, we determined the derivative to be

5. To differentiate a function f(x) which is the product of two functions g(x) and h(x) you…… Multiply the first function by the derivative of the second function then add The product of the second function and the derivative of the first If f(x) = g(x)h(x), then

6. f(x) = g(x)h(x)  f / (x) = g(x) h / (x) + h(x) g / (x) Example 1 Differentiate f(x) = x 2 sin x Let g(x) = and h(x) = g / (x) =h / (x) = f /(x) =f /(x) = In its simplest form: f / (x) =

7. Example Two - Differentiate