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# 7- Derivatives

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Department
Mathematics
Course Code
MAT135H1
Professor
all

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Derivatives     Knowledge  Summary:     1)  Constant  rule:  For  any  number  c,  if  f(x)=c  then  f’(x)=  0       2)  Power  rule:  For  any  constant  in  f(x),  bring  power  to  the  front,  then  reduce  power  by  1     f’(x)=  r  x    ­‐1   3)  Constant  multiple  rule:  For  any  coefficient  in  f( x),  bring  power  to  the  front,  then  reduce  power   by   1,  do  not  change  constant  (similar  to  power  rule,  but  used  when  there’s  a  coefficient  in  front  of   constant)     f’(x)=  c  g’(x)     4)  Sum  rule:  For  any  function  that  is  a  sum  of  different  terms,  take  the   derivative  of  each  term   separately   f’(x)=  g’(x)  +  h’(x)     5)  Difference  rule:  For  any  function  that  is  a  difference  of  different  terms,  take  the  derivative  of  each   term  separately   f’(x)=  g’(x)  -­‐  h’(x)     6)  Product  rule:  For  any  function  made  up  of  two  parts,  differentiate  one  and  rewrite  the  second   then  repeat  the  process  for  the  second  function     f’(x)  =  g(x)  h’(x)  +  h(x)  g’(x)     Step-­‐by-­‐Step:       1)  Constant  rule:     5)  Difference  rule:     3 -­‐2 3 -­‐2 f(x)=  -­‐10   f(x)=  x  -­‐  x ,  let  g(x)=  x  and  h(x)=  x     f’(x)=  0   f  '(x)=  g  '(x)  -­‐  h  '(x)                    =  3x  -­‐  (-­‐2x )     2 -­‐3   2)  Power  rule:              =  3  x  +  2x       f(x)=  x   2     f’(x)=  2x   6)  Product  rule:
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