g(x) = -500/x , x does not equal 0

Question

Compute the derivative (that is, the derivative function) by evaluating the limit

Answer 1

I assume you are the same "anonymous" as the one asking similar questions
below, so I will shorten this up a bit
g(x) = -500/x, then g(x+h) = -500/(x+h)

d(g(x))/dx = lim (-500/(x+h) - (-500/x) )/h as h ---> 0
= lim [ (-500x + 500(x+h) )/(x(x+h)) / h , .....
= lim[ -500x + 500x + 500h)/(x^2 + xh)] / h , ......
= lim 500/x^2 , as h ---->
= 500/x^2