1. Daily Warm-Up: Find the derivative of the following functions
Objectives:
Be able to find the derivative of functions by applying the Product Rule.
Critical Vocabulary:
Derivative, Tangent
Daily Warm-Up: Find the derivative of the following functions
1. h(x) = (3x - 2x2)(5 + 4x)
2. h(x) = x2(3x - 2)(x2 - 4x)

2. I. The Product Rule
The Product Rule is used when two or more functions are being multiplied together. h(x) = f(x) • g(x)
Look back at our warm-up problem: f(x) = (3x - 2x2)(5 + 4x)
This could be done using the PRODUCT RULE!!!!!
Example 1: Find the derivative: h(x) = (3x - 2x2)(5 + 4x)

3. I. The Product Rule
Example 2: Use the function to find the slope of the tangent
line at the point (2, 3/2)

4. I. The Product Rule
Example 3: Use the function to find the equation of the
tangent line at the point (-1, 4): h(x) = 2x(x2 + 3x)

5. I. The Product Rule
The Product Rule can be extended to more than 2 functions.
Example 4: Find the derivative: j(x) = x2(3x - 2)(x2 - 4x )

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