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MTH142_Assg02

# MTH142_Assg02 - 1 g x as g x-1 and using the product...

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Assignment 2 Exploring the rules for derivatives Due Monday, February 11, 2008 In each of the problems below, you are to compute the derivative of a certain function (like f ( x ) = 3 x ( x 2 - 1 x ) – see problem 1b) in two di ff erent ways. When you have done that, please verify your work by showing that your results are identical. (For example, in problem 1b, whether you use algebra or the product rule, you should eventually get the same derivative.) You may gain 2 points extra credit by sending me the solution to problem 1b by email before 11:59 PM, Wednesday, February 6, 2008. (You may just send me the answer – you don’t need to send me your work in that email.) 1. Compute the derivative of each of the functions below in two di ff erent ways. First use algebra to simplify the function followed by a simple derivative rule. After getting the derivative that way, recompute the derivative by using the product rule instead. (a) f ( x ) = x · x 2 . (b) f ( x ) = 3 x ( x 2 - 1 x ) . 2. Compute the derivative of each of the functions below in two di ff erent ways. First use the quotient rule. Then recompute the derivative by writing

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Unformatted text preview: 1 g ( x ) as ( g ( x ))-1 and using the product rule. (I’ve tried to make this second method clear by rewriting the function for you in each case.) (a) f ( x ) = sin( x ) x 2 = sin x · x-2 . (b) f ( x ) = x x 2 + x = ( x ) · ( x 2 + x )-1 . 3. Compute the derivative of each of the functions below in two di±erent ways. First use algebra (the “binomial theorem”) to expand the expression and apply a simple derivative formula. Then recompute the derivative by using the chain rule instead. (a) f ( x ) = ( x + 2) 3 . (b) f ( x ) = (3 x 2 + 1) 4 . Hints and Suggestions for Assignment 2 1. (a) Easy! (b) Write 3 √ x and 1 /x as powers of x . 2. (a) Straightforward. (b) Be willing to factor. 3. (a) Use Pascal’s triangle to write out ( A + B ) 3 . Here A = x and B = 2 so your answers will include powers of 2, like 4 or 8. (b) Use Pascal’s triangle to write out ( A + B ) 4 . Here A = 3 x 2 and B = 1....
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MTH142_Assg02 - 1 g x as g x-1 and using the product...

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