I have a problem on my homework.
What is the derivative of $5/x$ ?
And can you please explain.
Thank you.
I have a problem on my homework.
What is the derivative of $5/x$ ?
And can you please explain.
Thank you.
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 $n=-1$.
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