Derivative of -500/x, x ≠ 0?
I have a lot of problems like this, and if someone can just show me how to do one, then I could figure out the rest.
I know I have the first step right (teacher told me):
[(-500/(x+h)) – (-500/x)] / h
Any help is appreciated.
Update:Oh, I'm supposed to be calculating the derivative by finding the limit as h approaches 0.
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Verified answer
Lim [500/(x+h)-500/x]/h
h->0
=
Lim 500[(x-(x+h))/(x^2+xh)]/h
h->0
=
Lim 500[(-h)/(x^2+xh)]/h
h->0
=
Lim -500/(x^2+xh)
h->0
=
-500/x^2