chapter3(4) - MATH1010: Chapter 3 cont 1 DIFFERENTIATION...

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MATH1010: Chapter 3 cont… 1 DIFFERENTIATION RULES cont … Derivatives of Logarithmic Functions (Section 3.8, pg.244) Question: How do we differentiate logarithmic functions? Derivative of General Logarithmic Function: a x x dx d a ln 1 ) (log = Proof: Derivative of Natural Logarithm: x x dx d 1 ) (ln = Application: Based on data from a study (published in Nature in 1976), the average walking speed v (in ft/s) of a person living in a city of population x , may be modelled by 0255 . 0 log 873 . 0 ) ( 10 = x x v Find ) ( x v and interpret its meaning. [Source: “Calculus for the Life Sciences”, Greenwell, Ritchey, and Lial, 2003.] Example: + + 3 tan 1 5 ln 2 x x dx d
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Chapter 3 cont… 2 Finally, let’s consider a very useful technique for finding derivatives, which makes use of logarithmic functions. Steps for Logarithmic Differentiation : 1. Take logarithms of both sides of an equation 2. Simplify using logarithm rules 3. Differentiate implicitly with respect to x 4. Solve for the derivative, y . Example:
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chapter3(4) - MATH1010: Chapter 3 cont 1 DIFFERENTIATION...

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