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R2ps - Chapter 2 Derivatives and differentiation(Review...

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Chapter 2 Derivatives and differentiation. (Review) Stephen Suen Chapter 2 Derivatives and differentiation – p. 1/1
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2.1 The derivative and its mean- ing The slope of a secant line vs. the slope of a tangent line. The average rate of change vs. the instantaneous rate of change. See also §2.3. The definition of the derivative f ( x ) of a function f . Finding the derivative using the limit definition. Chapter 2 Derivatives and differentiation – p. 2/1
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2.2 Basic rules of differentiation The simple power rule: d dx x r = r x r 1 . The constant rule: d dx c = 0 . Differentiating a constant gives a 0 . The constant multiple rule: d dx ( c f ( x )) = c d dx f ( x ) . Constant multiple stays. Term-by-term differentiation is ok. Chapter 2 Derivatives and differentiation – p. 3/1
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2.3 Rates of change, marginals Recall: Average rate of change vs. instantaneous rate of change. Marginal revenue, marginal cost and marginal profit. The meaning of the marginals. Exercise 42. Chapter 2 Derivatives and differentiation – p. 4/1
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2.4 The product and quotient rules The product rule: d dx [( 1st )( 2nd )] = ( 1st ) × ( 2nd )+( 1st ) × ( 2nd ) .
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