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Unformatted text preview: 21A Calculus Monica Vazirani Nov 19, 2007 Midterm 2 Name: ID: Section: 1. (15 points) Calculate the following derivatives, using any method you choose (power rule, product rule, quotient rule, chain rule, logarithmic differentiation, memorization, etc). You MUST show your work for full credit. (If it is a memorized formula, state so.) a. d dx ( x √ 3 ) Solution: √ 3 x √ 3 1 b. d dx (( √ 3) x ) Solution: = d dx ( e x 1 2 ln 3 ) = ( ln 3 2 ) e x 1 2 ln 3 = ( ln 3 2 )( √ 3) x c. d dx (log 3 ( x 2 )) Solution: = d dx ln( x 2 ) ln 3 = d dx 2 ln 3 ln x = 2 ln 3 1 x 2. (10 points) Calculate the following derivatives, using any method you choose. You do NOT need to simplify answers (do not need to expand nor distribute products, or simplify fractions, or put a sum of fractions on common denominators). In fact,you are encouraged to not simplify. a. d dx (ln( 7 x 3 e 4 x ( x 3)(2 x +1) )) Solution: = d dx (ln 7 + 3 ln x + 4 x ln( x 3) ln(2 x + 1)) = 0 + 3 x + 4 1 x 3 2 2 x +1 b.b....
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This note was uploaded on 10/07/2008 for the course MATH 21A taught by Professor Osserman during the Spring '07 term at UC Davis.
 Spring '07
 Osserman
 Chain Rule, Derivative, Power Rule, Product Rule, Quotient Rule

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