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# Copy_of_3.9_notes - c How fast was the flu spreading after...

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Calculus Section 3.9 Page 48 3.9 Derivatives of Exponential and Logarithmic Fcns Derivative of y = e x Graph Y 1 = e x . Then graph the derivative of this function using the numerical derivative feature of your calculator: Y 2 = nDeriv Y 1 , X , X ( ) What do you notice? e x ( ) = e u ( ) = Example 1 Find the derivative of each function: a) y = e 3 x b) y = e x 3 c) y = e x d) y = e 4 - x e) y = e sin x f) y = e tan - 1 x g) y = xe x h) y = x 2 e x Example 2 How Fast does a Flu Spread? The spread of a flu in a certain school is modeled by the equation P t ( ) = 100 1 + e 3 - t where P t ( ) is the total number of students infected t days after the flu was first noticed.

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Calculus Section 3.9 Page49 a) Graph the function P t ( ) in the window shown. - 5,10 [ ] by - 25, 120 [ ] b) Estimate the initial number of students infected with the flu.
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Unformatted text preview: c) How fast was the flu spreading after 3 days? d) Graph the derivative; when will the flu spread at its maximum rate? What is this rate? -5,10 [ ] by-10, 30 [ ] Derivative of y = ln x To determine the derivative of the natural log function, change to exponential form and differentiate implicitly. y = ln x Calculus Section 3.9 Page 50 ln x ( ) ′ = ln u ( ) ′ = Example 3 Find the derivative of each function: a) y = ln x 2 b) y = ln 3 x c) y = ln 3 x + 3 ( ) d) y = ln x 2 + 5 ( ) e) y = ln sin x ( ) f) y = ln x ( ) 2 g) y = x ln x h) y = ln ln x ( ) Assignment II–9 Pages 170 #1 – 10 all, 21 – 30 all, 41, 42, 48...
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Copy_of_3.9_notes - c How fast was the flu spreading after...

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