# Finding the derivative of $5/x$

I have a problem on my homework.
What is the derivative of $5/x$ ?

Thank you.

-
What have you tried so far? –  Owen Biesel Sep 27 '12 at 15:46
nothing , I don't know where to start from. –  Cioroianu Denis Sep 27 '12 at 15:48
We don't know where to start either. Do you know any derivative rules? Do you have to find the derivative using only the definition of derivative? –  David Mitra Sep 27 '12 at 15:51

Use the power rule as normal and use the following result:

$\frac{d}{dx}(\frac{a}{x}) =a\times\frac{d}{dx}(\frac{1}{x})$

This yields $\frac{d}{dx}(\frac{5}{x})=5\times\frac{d}{dx}(\frac{1}{x}) =5\times \frac{d}{dx}(x^{-1})$ $5\times(-1)x^{-2}=-\frac{5}{x^2}$.

Hope that helps.

-

First, it helps to rewrite fractions using negative exponents, so $\frac{5}{x}=5x^{-1}$. Now you can use the power rule to calculate the derivative with $n=-1$.

-
thanks for the hint , I realized it now . –  Cioroianu Denis Sep 27 '12 at 15:50
You should evaluate $\lim_{h\to 0} \dfrac{ f(x+h)-f(x)}{h}$.