practice2sol - MAT 21A Fu Liu Practice Exam 2 1 (42 pts.)...

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Unformatted text preview: MAT 21A Fu Liu Practice Exam 2 1 (42 pts.) Differentiate the following functions. Show your work if you wish to receive partial credit. You do not need to simplify your answers. (The step where I marked with a ? is the place where you can finish as an answer.) (a) f ( x ) = 3 x +7 x 4 +1 . Solution : f ( x ) = x 4 + 1 d dx (3 x + 7)- (3 x + 7) d dx ( x 4 + 1) x 4 + 1 = 3 x 4 + 1- (3 x + 7) 1 2 x 4 +1 d dx ( x 4 + 1) x 4 + 1 = 3 x 4 + 1- (3 x + 7) 2 x 3 x 4 +1 x 4 + 1 ? =- 3 x 4- 14 x 3 + 3 ( x 4 + 1) 3 / 2 (b) f ( x ) = sec 2 ( x + sin x ) . Solution : f ( x ) = 2 sec( x + sin x ) d dx (sec( x + sin x )) = 2 sec( x + sin x ) sec( x + sin x ) tan( x + sin x ) d dx ( x + sin x ) = 2 sec 2 ( x + sin x ) tan( x + sin x )(1 + cos x ) ? (c) f ( x ) = e 2 x- 1 x + 1 . Solution : f ( x ) = e 2 x- 1 d dx ( x + 1) + x + 1 d dx ( e 2 x- 1 ) = e 2 x- 1 1 2 x + 1 d dx ( x + 1) + x + 1 e 2 x- 1 d dx (2 x- 1) = e 2 x- 1 1 2 x + 1 + 2 x + 1 e 2 x- 1 ? = e 2 x- 1 4 x + 5 2 x + 1 (d) f ( x ) = 1 (ln x ) 10 . Solution : f ( x ) = (ln x )- 10 ....
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This note was uploaded on 03/25/2010 for the course MATH math 21A taught by Professor Fuliu during the Winter '10 term at UC Davis.

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practice2sol - MAT 21A Fu Liu Practice Exam 2 1 (42 pts.)...

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