Question

How do you find the derivative of `y(x)= 6/(x-8)`?

Answer 1

`y'(x)=(-6)/(x-8)^2`

Explanation:

We will find `y'(x)` based on derivative of rational function that says:
`color(blue)((u/v)'=(u'v-v'u)/v^2`

`color(blue)(y'(x)=((6)'(x-8)-(x-8)'*6)/(x-8)^2`

`color(blue)(y'(x)=(0*(x-8)-1*6)/(x-8)^2`

`color(blue)(y'(x)=(-6)/(x-8)^2`