Question

How do you find the derivative of `1/(x-5)`?

Answer 1

Use `1/a=a^-1` and chain rule. It's `-1/(x-5)^2`

Explanation:

`1/(x-5)=(x-5)^-1`

The chain rule:

`((x-5)^-1)'=-1*(x-5)^(-1-1)*(x-5)'=`

`=-(x-5)^-2*1=-1/(x-5)^2`

Note: the chain rule does not make a difference in this case. However, if there was another function in which the denominator which didn't have a derivative equal to 1, the differentiation process would be more complex.