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Taking the derivative of products, Feb. 17, simplify first. Feb. 20, Power rule, chain rule. Quadratic, tangent slopes will not be the same for all x ε.

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Presentation on theme: "Taking the derivative of products, Feb. 17, simplify first. Feb. 20, Power rule, chain rule. Quadratic, tangent slopes will not be the same for all x ε."— Presentation transcript:

1 Taking the derivative of products, Feb. 17, simplify first. Feb. 20, Power rule, chain rule. Quadratic, tangent slopes will not be the same for all x ε R Product of linear functions Does the derivative depend upon the derivative of the individual linear functions? YES But don’t just take the derivative of each factor. Using the “Product rule” Derivative of the 1 st factor 2 nd factor Derivative of the 2nd factor 1 st factor

2 The derivative of h(x) with respect to “x” is the derivative of the first factor, times the second factor + plus the derivative of the second factor, times the first factor. The first factor The second factor Differentiation using the product rule

3 Example s: Given:then [][] [][] + [][] 3 [][] If you were to simplify the derivative, you would drop brackets using multiplication and then collect like terms. The textbook simplifies their answers. [ ] [][] + [][][][] 3 Now simplify the derivative or

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