# Calculus (Derivatives)

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What is the derivative of the this functon?
g(x) = -500/x, x cannot equal 0.

I know that in order to fnd the derivative I need to put the function into the equation for evaluating derivatives as limits.
lim as h -> 0 (f(x+h) - f(x))/h
I did this, but I am having difficulties simplifying it to evaluate the limit. Any help at all is appreciated!

• Calculus (Derivatives) -

Let K= -500

lim (K/(x+h) - K/x)/h

lim K (x-x-h)/x(x+h)h
= -K (h/x(x+h)h=lim -K 1/x(x+h)
= -k/x^2
= 500/x^2

• Calculus (Derivatives) -

Okay. So, 500/x^2 would be the simplified equation for the derivative, and from here I can figure that the limit is 5,000,000 as h approaches 0. Is this correct?

• Calculus (Derivatives) -

I too was able to come to the derivative of 500/x^2

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