I don't whether this is a derivative or what. But i will show you how to get the derivative of it.

lets call it y,

y = `(-x^2-2x+8)/(x+4)^4`

You can use the following rule of differentiation.

`(d(u/v))/dx = (v(du)/(dx) - u(dv)/(dx))/(V^2)`

so,

`(dy)/(dx) = ((x+4)^4 * (-2x-2) - (-x^2-2x+8)*4*(x+4)^3)/(x+4)^8`

`(dy)/(dx) = ((x+4) * (-2x-2) - (-x^2-2x+8)*4)/(x+4)^5`

`(dy)/(dx) = (-2x^2-8x-2x-8 - (-4x^2-8x+32))/(x+4)^5`

`(dy)/(dx) = (-2x^2-8x-2x-8 +4x^2+8x-32)/(x+4)^5`

`(dy)/(dx) = (2x^2-2x-40)/(x+4)^5`