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

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


   

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) About Me  (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