Find the derivative f(x)= 1/(x-1)

Question

I need help finding the derivative of this question. I'm not sure what to do adter getting the least common denominator the same. 

Answer 1

Use the exponent rule and the chain rule:

 

f(x) = (x - 1)^-1

 

f'(x) = -(x - 1)^-1-1 d/dx (x - 1)

 

f'(x) = - 1 / (x - 1)²

Answer 2

You can also use quotient rule.

 

f'(x) = [1'(x - 1) - 1(x - 1)'] / (x - 1)²

 

 

Note:  Single quotations mean derivative.