Question

How do you find the derivative of `(2x+8)/(x-8)`?

Answer 1

`d/dx((2x+8)/(x-8)) = (-24)/(x-8)^2`

Explanation:

You need to use the quotient rule; `d/dx(u/v) = (v(du)/dx-u(dv)/dx)/v^2`

`d/dx((2x+8)/(x-8)) = ((x-8)d/dx(2x+8) - (2x+8)d/dx(x-8))/(x-8)^2`
`:. d/dx((2x+8)/(x-8)) = ((x-8)(2) - (2x+8)(1))/(x-8)^2`
`:. d/dx((2x+8)/(x-8)) = (2x-16-2x-8)/(x-8)^2`
`:. d/dx((2x+8)/(x-8)) = (-24)/(x-8)^2`