The Product Rule. Do Now  Find the derivative of f(x) = x(x 2 + 2x – 1).  What is the derivative of sinx? of cosx?

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Presentation transcript:

The Product Rule

Do Now  Find the derivative of f(x) = x(x 2 + 2x – 1).  What is the derivative of sinx? of cosx?

Thm. 2.7: The Product Rule  The product of two differentiable functions, f and g, is itself differentiable. Moreover, the derivative of f  g is the first function times the derivative of the second plus the second function times the derivative of the first.

Extension of the Product Rule  For three functions,

Ex. 1  Find the derivative of y = x 2 sinx cosx.

Ex. 2  Find the derivative of h(x) = (3x – 2x 2 )(5 + 4x).

Ex. 3  Find the derivative of y = 3x 2 sinx.

Ex. 4: Product and Difference  Find the derivative of y = 2x cosx – 2 sinx.

Ex. 5  Redo the Do Now problem using the product rule: f(x) = x(x 2 + 2x – 1).