Homework, Page 170 Find an equation of the tangent line at the point indicated. 1. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 170 Find the derivative of each function. 5. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 170 Find the derivative of each function. 9. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 170 Find the derivative of each function. 13. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 170 Find the derivative of each function. 17. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 170 Find the derivative of each function. 21. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 170 Find the derivative of each function. 25. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 170 Calculate the second derivative. 29. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 170 Find an equation of the tangent line at the point specified. 33. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 170 Find an equation of the tangent line at the point specified. 37. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 170 Find an equation of the tangent line at the point specified. 37. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 170 Verify the formula. 41. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 170 43. Calculate the first five derivatives of f (x) = cos x. Then determine f (8) and f (37). Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 170 45. Calculate f ′(x) and f ′″(x) where f (x) = tan x Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Homework, Page 170 49. The height at time t (s) of a weight, oscillating up and down at the end of a spring, is s(t) = 300 + 40 sin t cm. Find the velocity and acceleration at t = π/3 s. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Chapter 3: Differentiation Section 3.7: The Chain Rule Jon Rogawski Calculus, ET First Edition Chapter 3: Differentiation Section 3.7: The Chain Rule Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Composite Functions Composite functions are combinations of simpler functions, for instance f (x) = sin ex. None of the rules of differentiation we learned thus far permit us to differentiate a composite function. Remembering that the composition of f (x) and g (x) is written as f ○ g (x) or f (g (x)), we use the Chain Rule to differentiate composites. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

If we choose, we may also represent a composite function of f (x) and u (x) as f (u). The chain rule then becomes: which may also be written as: Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Example, Page 178 8. Calculate d/dx f (x2 + 1) for the following choices of f (u ): Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Example, Page 178 8. Calculate d/dx f (x2 + 1) for the following choices of f (u ): Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Example, Page 178 Find the derivative of f ○ g. 16. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

Example, Page 178 Find the derivative of f ○ g. 16. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

WS 3.7.pdf Rogawski Calculus Copyright © 2008 W. H. Freeman and Company