3.2   The Quotient Rule

EXERCISES


1.   Suppose that the derivative of “fi” is “fo”,
      and the derivative of “fo” is the negative of “fi”.  
      Then what’s the derivative of “fi” over “fo”?


2.   Suppose that f ’(x) = 3g(x)  and  g’(x) = –2f (x). 

      Find the derivative of  f (x)/g(x).


3.   Suppose that M ’(x) = W(x) – M(x)   and  W ’(x) = M(x) – W(x). 

      Find the derivative of  M(x)/W(x).


4.   Suppose that  T(0) = 3,  T ’(0) = 5,  B(0) = –2, and   B’(0) = –1. 

      Find the derivative of  T(x)/B(x), evaluated at x=0.


5.   Suppose that  f(1) = –2,  f ’(1) = 1/3,  g(1) = 3, and   g’(1) = 1/2. 

      Let  Q(x) = f(x)/g(x).    Then  Q’(1) = ?


6.   Suppose that  f(3) = 10,  f ’(3) = 1/4,  g(3) = 20, and   g’(3) = –1/5. 

      Let  R(x) = f(x)/g(x).    Then  R’(3) = ?


7.  


8.  


In problems #9 and #10, try to find a way to do the problems without resorting to the quotient rule.


9.  


10.  


11.  (Warning: not for the faint of heart! 


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© 1998-2003 by
Rafael Espericueta
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