R2 - Chapter 2 Derivatives and differentiation(Review...

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Unformatted text preview: Chapter 2 Derivatives and differentiation. (Review) Stephen Suen Chapter 2 Derivatives and differentiation – p. 1/1 5 2.1 The derivative and its mean- ing • The slope of a secant line vs. the slope of a tangent line. Chapter 2 Derivatives and differentiation – p. 2/1 5 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. Chapter 2 Derivatives and differentiation – p. 2/1 5 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 . Chapter 2 Derivatives and differentiation – p. 2/1 5 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 5 2.2 Basic rules of differentiation • The simple power rule: d dx x r = r x r − 1 . Chapter 2 Derivatives and differentiation – p. 3/1 5 2.2 Basic rules of differentiation • The simple power rule: d dx x r = r x r − 1 . • The constant rule: d dx c = . Differentiating a constant gives a . Chapter 2 Derivatives and differentiation – p. 3/1 5 2.2 Basic rules of differentiation • The simple power rule: d dx x r = r x r − 1 . • The constant rule: d dx c = . Differentiating a constant gives a . • The constant multiple rule: d dx ( c f ( x )) = c d dx f ( x ) . Constant multiple stays. Chapter 2 Derivatives and differentiation – p. 3/1 5 2.2 Basic rules of differentiation • The simple power rule: d dx x r = r x r − 1 . • The constant rule: d dx c = . Differentiating a constant gives a . • 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 5 2.3 Rates of change, marginals • Recall: Average rate of change vs. instantaneous rate of change. Chapter 2 Derivatives and differentiation – p. 4/1 5 2.3 Rates of change, marginals • Recall: Average rate of change vs. instantaneous rate of change. • Marginal revenue, marginal cost and marginal profit. Chapter 2 Derivatives and differentiation – p. 4/1 5 2.3 Rates of change, marginals • Recall: Average rate of change vs. instantaneous rate of change. • Marginal revenue, marginal cost and marginal profit....
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This note was uploaded on 01/02/2012 for the course MAC 2233 taught by Professor Danielyan during the Fall '08 term at University of South Florida.

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R2 - Chapter 2 Derivatives and differentiation(Review...

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