2021-06-01

What formula do we need, in addition to: $\frac{d}{dx}\left({x}^{n}\right)=n{x}^{n-1}$
$\frac{d}{dx}\left(cu\right)=cd\frac{u}{dx}$
$\frac{d}{dx}\left({u}_{1}+{u}_{2}+\dots +{u}_{n}\right)=d\frac{{u}_{1}}{dx}+d\frac{{u}_{2}}{dx}+\dots +d\frac{{u}_{n}}{dx}$ to differentiate rational functions?

Tasneem Almond

Since rational function include fractions, we need the following formula for differentiating rational functions: $\frac{d}{dx}\frac{f\left(x\right)}{g\left(x\right)}=\left(\frac{\left(d\frac{f}{dx}\right)\left(x\right)g\left(x\right)-f\left(x\right)\left(d\frac{g}{dx}\right)x}{{g}^{2}\left(x\right)}$