WkSheet1 - u )] =-sin( u ) [ x 2 cos( x 2 )] = [ x 2 ]...

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Calculating Derivatives I Name: M408C, 59105/59110/59115 September 25, 2007 List the derivative rules (I count 4) we have learned so far, and write the corresponding for- mula: 1) Power Rule: f ( x ) = x n = f 0 ( x ) = 2) 3) 4) List the trig functions with derivatives we know (I count 3), and write those derivatives: 1) f ( x ) = sin( x ) = f 0 ( x ) = 2) 3) Now calculate the following derivatives. It might help to write out which rules you will use, as well as which trig functions. Try to keep your work concise, systematic, and NEAT! 1) f ( x ) = x 2 cos( x 2 ) Product Rule, Chain Rule, Power Rule , [cos(
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Unformatted text preview: u )] =-sin( u ) [ x 2 cos( x 2 )] = [ x 2 ] [cos( x 2 )] + [cos( x 2 )] [ x 2 ] Product Rule = [2 x ][cos( x 2 )] + [cos( x 2 )] [ x 2 ] Power Rule = [2 x ][cos( x 2 )] + [-sin( x 2 ) 2 x ][ x 2 ] Chain Rule = 2 x cos( x 2 )-2 x 3 sin( x 2 ) Simplify 2) f ( x ) = sin(3 x 2 + x ) + x 2 + 1 3) f ( x ) = x 3 tan( x 4 + x ) 4) y = cos(sin(-x )) cos(cos(-2 x 3 )) 5) g ( x ) = x 3 sin 2 (3 x 2 ) Challenge) f ( x ) = x 2 sin( x 3 ) cos(4 x-3) sin(sec( x ))...
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This note was uploaded on 03/20/2008 for the course M 408c taught by Professor Mcadam during the Spring '06 term at University of Texas at Austin.

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WkSheet1 - u )] =-sin( u ) [ x 2 cos( x 2 )] = [ x 2 ]...

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