I'm having trouble with differentials. I've been trying to learn about them online using great resources like PatrickJMT but I'm having trouble finding examples for this kind or problem. I hate asking questions when I don't have any work to show but I'd like some help to get started.
Find the differential of the following function: $$y = \frac{u+1}{u-1}$$
If someone could show me how to begin or link me to some information on the web, that would be great!
On
Depends on your knowledge of differentials and derivatives. In most of the cases, you are taught about differentials via derivatives, and for functions of one variable you always get $$ dy(u) = y'(u)du. $$ So you only have to compute the derivative $y'(u)$ e.g. via the derivative rule for fractions, and put $du$ from the right of that.
$$\frac{dy}{du}=\frac{d}{du} \left ( \frac{u+1}{u-1}\right )=\frac{u-1-u-1}{(u-1)^2}=\frac{-2}{(u-1)^2}$$
$$dy=\frac{-2}{(u-1)^2} du$$