midterm2.s2

midterm2.s2 - 21A Calculus Monica Vazirani Midterm 2 Name...

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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 √ 7 ) Solution: √ 7 x √ 7- 1 b. d dx (( √ 7) x ) Solution: = d dx ( e x 1 2 ln 7 ) = ( ln 7 2 ) e x 1 2 ln 7 = ( ln 7 2 )( √ 7) x c. d dx (log 7 ( x 2 )) Solution: = d dx ln( x 2 ) ln 7 = d dx 2 ln 7 ln x = 2 ln 7 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( 3 x 7 e 4 x ( x- 7)(2 x +1) )) Solution: = d dx (ln 3 + 7 ln x + 4 x- ln( x- 7)- ln(2 x + 1)) = 0 + 7 x + 4- 1 x- 7- 2 2 x +1 b.b....
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midterm2.s2 - 21A Calculus Monica Vazirani Midterm 2 Name...

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