-2
$\begingroup$

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

Thank you.

  • 1
    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?2012-09-27

3 Answers 3

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.

1

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 $n=-1$.

  • 0
    thanks for the hint , I realized it now .2012-09-27
1

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

  • 1
    @Patrick: I read the OP's comment to his question where he said that he didn't know where to begin. I think my answer gives that start. And I would be happy if others were willing to offer additional assistance if the OP asked, as the latter half of my answer does. In short, I defend this answer as an answer, not as a comment.2012-09-28