Section 3.1 Derivative Formulas for Powers and Polynomials

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Presentation transcript:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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