Finding the derivative of $5/x$

Question

I have a problem on my homework.
What is the derivative of $5/x$ ?
And can you please explain.

Thank you.

Answer 1

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.

Answer 2

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 $n=-1$.

Answer 3

You should evaluate $\lim_{h\to 0} \dfrac{ f(x+h)-f(x)}{h}$.

If you run into trouble with calculation, show us your work and we can proceed from there