Warm up: Find the derivative of the following. Question: Can we find the derivative of a product by multiplying the two derivatives? Test this with some.

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Presentation transcript:

Warm up: Find the derivative of the following

Question: Can we find the derivative of a product by multiplying the two derivatives? Test this with some examples to see if it works.

Product Rule for Derivatives Section 2.3

Product of two functions Find the derivative of f(x)g(x):

Product of two functions Find the derivative of f(x)g(x): Find the following: f’(x)g(x) + g’(x)f(x) What do you notice?

Product Rule for a Derivative Proof: What is the derivative of h(x) = f(x) g(x)?

Practice: Using the Product Rule Find the derivative of the following functions:

Extending the Product Rule Find the derivative of

Extending the Product Rule a)Find the derivative of b)Find the derivative of

The Power of a Function Rule The derivative of Is given by

The Power of a Function Rule The derivative of Is given by Eg) Find the derivative of:

Challenge: Find the derivative of the following, using the product rule

Summary: What is the product rule? What is the power of a function rule? How can we find the derivative of the product of three functions? Practice: pg. 90, #2, 5, 7, 11, 12