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The Product Rule
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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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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.
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Extension of the Product Rule For three functions,
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Ex. 1 Find the derivative of y = x 2 sinx cosx.
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Ex. 2 Find the derivative of h(x) = (3x – 2x 2 )(5 + 4x).
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Ex. 3 Find the derivative of y = 3x 2 sinx.
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Ex. 4: Product and Difference Find the derivative of y = 2x cosx – 2 sinx.
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Ex. 5 Redo the Do Now problem using the product rule: f(x) = x(x 2 + 2x – 1).
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