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1ls3_lectures1617 - Announcements Topics...

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Announcements Topics: ‐ sec0ons 4.1 – 4.5 (differen0a0on rules), 4.6 * Read these sec0ons and study solved examples in your textbook! Work On: ‐ Prac0ce problems from the textbook and assignments from the coursepack as assigned on the course web page (under the link “SCHEDULE + HOMEWORK”)
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Using the Deriva0ve to Sketch the Graph of a Func0on Example 4.1, #18. Sketch the graph of g ( x ) = 4 x x 2 . y x
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Chain Rule “deriva0ve of the outer func0on evaluated at the inner func0on 0mes the deriva0ve of the inner func0on” Example: Differen0ate the following. (a) (b) [ f ( g ( x ))]' = f '( g ( x )) g '( x ) f ( x ) = (4 x 3 + 1) 10 g ( x ) = 1 x 2 + 1
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Chain Rule Example 4.5, #58 . The number of mosquitoes ( M ) that end up in a room is a func0on of how far the window is open ( W , in square cen0metres) according to The number of bites ( B ) depends on the number of mosquitoes according to Find the deriva0ve of B as a func0on of W . M ( W ) = 5 W + 2. B ( M ) = 0.5 M .
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Deriva0ve of the Natural Exponen0al Func0on Defini&on: The number e is the number for which Natural Exponen0al Func0on : y x f ( x ) = e x f ( x ) = e x lim h 0 e h 1 h = 1
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