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Differentiate f(x)= 6-xe^x/x+e^x

Differentiate f(x)= 6-xe^x/x+e^x

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Robert A. | Certified Teacher and Engineer - Tutoring Physics, Maths, and SciencesCertified Teacher and Engineer - Tutorin...
5.0 5.0 (114 lesson ratings) (114)
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Assuming exactly the way you typed it in:
 
(I assumed no extra parenthesis and used a strict order of operations.)
 
d/dx [ 6 - (xex/x) + ex ]
 
the expression  [ 6 - (xex/x) + ex ]  =  [ 6 - ex + ex ] = 6
 
so d/dx (6) = 0
 
Of course if you really meant it as:
 
f(x) = (6-ex)/(x + ex)    then it is 
 
f'(x)' = [ ex(x2 + 6) + e2x + 6 ] / (x+ex)2

  Note: it is f (x)  or f(x) == f prime(x) == not f(x)
 
If you meant something else ask again letting us know where the parenthesis go.
William S. | Experienced scientist, mathematician and instructor - WilliamExperienced scientist, mathematician and...
4.4 4.4 (10 lesson ratings) (10)
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f(x) = (6-ex)/(x + ex)
 
f'(x) = ex(x2 + 6) + e2x + 6
          _________________
                   (x+ex)2