# How do you differentiate #f(x)=(x-5)/(x-3)^2# using the quotient rule?

##### 1 Answer

Dec 18, 2015

#### Explanation:

How to differentiate using the quotient rule?

Given

#=((x-3)^2(1) -(x-5)(2(x-3)(1)))/(x-3)^4#

#=(color(red)((x-3))(x-3) -2color(red)((x-3))(x-5))/(color(red)((x-3))(x-3)^3)#

Factor out the greatest common factor

#f'(x) = ((x-3)-2(x-5))/(x-3)^3#

#= (x-3-2x+10)/(x-3)^3#

#f'(x)=(-x+7)/(x-3)^3 = -(x-7)/(x-3)^3#