Question

How do you use the quotient rule to differentiate `x^6/(x-6)`?

Answer 1

`f'(x)=(5x^6-36x^5)/(x-6)^2`

Explanation:

Let `f=x^6 and g=x-6`

Then`f'=6x^5 and g'=1`

Quotient Rule:
`f'(x)=(gf'-fg')/g^2`

`f'(x)=((x-6)(6x^5)-(x^6))/(x-6)^2`

`=(6x^6-36x^5-x^6)/(x-6)^2`

`=(5x^6-36x^5)/(x-6)^2`