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Section 3.1 Derivative Formulas for Powers and Polynomials

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1 Section 3.1 Derivative Formulas for Powers and Polynomials
Applied Calculus ,4/E, Deborah Hughes-Hallett Copyright 2010 by John Wiley and Sons, All Rights Reserved

2 Figure 3.1 A constant function
Applied Calculus ,4/E, Deborah Hughes-Hallett Copyright 2010 by John Wiley and Sons, All Rights Reserved

3 Applied Calculus ,4/E, Deborah Hughes-Hallett
Copyright 2010 by John Wiley and Sons, All Rights Reserved

4 Applied Calculus ,4/E, Deborah Hughes-Hallett
Copyright 2010 by John Wiley and Sons, All Rights Reserved

5 Applied Calculus ,4/E, Deborah Hughes-Hallett
Copyright 2010 by John Wiley and Sons, All Rights Reserved

6 Problem 39 Let Find f’(t) f (t) = t2 – 4t + 5. Find f’(1) and f’(2)
Use a graph of f(t) to check that your answers to part (b) are reasonable. Explain. f (t) = t2 – 4t + 5. Applied Calculus ,4/E, Deborah Hughes-Hallett Copyright 2010 by John Wiley and Sons, All Rights Reserved

7 Section 3.2 Exponential and Logarithmic Functions
Applied Calculus ,4/E, Deborah Hughes-Hallett Copyright 2010 by John Wiley and Sons, All Rights Reserved

8 Applied Calculus ,4/E, Deborah Hughes-Hallett
Copyright 2010 by John Wiley and Sons, All Rights Reserved

9 Differentiate the functions in Problems 1 – 28
Differentiate the functions in Problems 1 – 28. Assume that A, B, and C are constants. 3. y = 5 t2+ 4 et y = t2 + 5 ln t 19. Applied Calculus ,4/E, Deborah Hughes-Hallett Copyright 2010 by John Wiley and Sons, All Rights Reserved

10 Section 3.3 The Chain Rule Applied Calculus ,4/E, Deborah Hughes-Hallett Copyright 2010 by John Wiley and Sons, All Rights Reserved

11 Example 2 Solution Applied Calculus ,4/E, Deborah Hughes-Hallett
Copyright 2010 by John Wiley and Sons, All Rights Reserved

12 Example 6 (continued on next page)
Applied Calculus ,4/E, Deborah Hughes-Hallett Copyright 2010 by John Wiley and Sons, All Rights Reserved

13 Example 6 (continued) Applied Calculus ,4/E, Deborah Hughes-Hallett
Copyright 2010 by John Wiley and Sons, All Rights Reserved

14 Section 3.4 The Product and Quotient Rules
Applied Calculus ,4/E, Deborah Hughes-Hallett Copyright 2010 by John Wiley and Sons, All Rights Reserved

15 Applied Calculus ,4/E, Deborah Hughes-Hallett
Copyright 2010 by John Wiley and Sons, All Rights Reserved

16 Example 1 Solution Applied Calculus ,4/E, Deborah Hughes-Hallett
Copyright 2010 by John Wiley and Sons, All Rights Reserved

17 Applied Calculus ,4/E, Deborah Hughes-Hallett
Copyright 2010 by John Wiley and Sons, All Rights Reserved

18 Section 3.5 Derivatives of Periodic Functions
Applied Calculus ,4/E, Deborah Hughes-Hallett Copyright 2010 by John Wiley and Sons, All Rights Reserved

19 Applied Calculus ,4/E, Deborah Hughes-Hallett
Copyright 2010 by John Wiley and Sons, All Rights Reserved

20 Example 4 Solution Applied Calculus ,4/E, Deborah Hughes-Hallettt
Copyright 2010 by John Wiley and Sons, All Rights Reserved


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