SOLUTION: Using Limits to Calculate a Derivative Use the definition of the derivative to find f ′(x) if f(x)= 1/(x-1)

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Question 1010141: Using Limits to Calculate a Derivative
Use the definition of the derivative to find f ′(x) if
f(x)= 1/(x-1)

Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!



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Use f(x) to find f(x+h)








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Compute the difference quotient


























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The difference quotient is


Now evaluate the limit as h goes to 0. Since we no longer have to worry about division by zero errors, this is the equivalent to plugging in h = 0 to get





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So the derivative of f(x) is f ' (x) =

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