SOLUTION: Using Limits to Calculate a Derivative The derivative of f(x)= 1/(x-1) is f(x) = -1/(x-1)^2

SOLUTION: Using Limits to Calculate a Derivative The derivative of f(x)= 1/(x-1) is f(x) = -1/(x-1)^2

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Question 1010488: Using Limits to Calculate a Derivative
The derivative of
f(x)= 1/(x-1)
is
f(x) = -1/(x-1)^2

Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
f(x) = 1 / (x-1)
f'(x) = ((1/(x+h-1) - 1/(x-1)) / h
f'(x) = (x-1) - (x+h-1) / h(x-1)(x+h-1)
f'(x) = -h / h(x-1)(x+h-1)
f'(x) = -1/(x-1)(x+h-1)
limit as h--->0 f'(x) = -1 / (x-1)^2

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