1. Homework, Page 170
Find an equation of the tangent line at the point indicated. 1.
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2. Homework, Page 170 Find the derivative of each function. 5.
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3. Homework, Page 170 Find the derivative of each function. 9.
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4. Homework, Page 170 Find the derivative of each function. 13.
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5. Homework, Page 170 Find the derivative of each function. 17.
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6. Homework, Page 170 Find the derivative of each function. 21.
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7. Homework, Page 170 Find the derivative of each function. 25.
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8. Homework, Page 170 Calculate the second derivative. 29.
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9. Homework, Page 170
Find an equation of the tangent line at the point specified. 33.
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10. Homework, Page 170
Find an equation of the tangent line at the point specified. 37.
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11. Homework, Page 170
Find an equation of the tangent line at the point specified. 37.
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12. Homework, Page 170 Verify the formula. 41. Rogawski Calculus
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13. Homework, Page 170
43. Calculate the first five derivatives of f (x) = cos x. Then determine f (8) and f (37).
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14. Homework, Page 170
45. Calculate f ′(x) and f ′″(x) where f (x) = tan x
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15. 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) = sin t cm. Find the velocity and acceleration at t = π/3 s.
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16. Chapter 3: Differentiation Section 3.7: The Chain Rule
Jon Rogawski Calculus, ET First Edition
Chapter 3: Differentiation
Section 3.7: The Chain Rule
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17. 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.
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18. 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:
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19. Example, Page 178
8. Calculate d/dx f (x2 + 1) for the following choices of f (u ):
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20. Example, Page 178
8. Calculate d/dx f (x2 + 1) for the following choices of f (u ):
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21. Example, Page 178 Find the derivative of f ○ g. 16. Rogawski Calculus
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22. Example, Page 178 Find the derivative of f ○ g. 16. Rogawski Calculus
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23. WS 3.7.pdf Rogawski Calculus
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