simplify the compound fraction: ((x+h)^(-3)-x^(-3))/(h)
((x+h)^(-3)-x^(-3))/(h)
= ( 1/(x^3 + 3x^2h + 3xh^2 + h^3) - 1/x^3) )/h
common denominator at the top
= ( (x^3 - x^3 - 3x^2h - 3xh^2 - h^3)/(x^3(x^3 + 3x^2h + 3xh^2 + h^3) )/h
= ( -3x^2 - 3xh - h^2)/(x^3(x^3 + 3x^2h + 3xh^2 + h^3) )
checking:
if I let h = 0 this reduces to
-3x^2 /(x^3(x^3 + 0+0+0)
= -3/x^4 , which is the derivatiave of x^-3