Question

How do you differentiate `f(x)= (x+5)/ (x- 7 )` using the quotient rule?

Answer 1

`f'(x)=-12/(x-7)^2`

Explanation:

Given:

`f(x)=(N(x))/(D(x))`

`f'(x)=(N'(x)*D(x)-D'(x)*N(x))/((D(x))^2)`

Then:

`f'(x)=(1*(x-7)-1*(x+5))/(x-7)^2=(cancel(x)-7cancel(-x)-5)/(x-7)^2=`
`=-12/(x-7)^2`