Cho \(a,b,c>0\). Chứng minh:
\(\frac{{a}^{2}+{b}^{2}}{a+b}+\frac{{b}^{2}+{c}^{2}}{b+c}+\frac{{c}^{2}+{a}^{2}}{c+a}\geq{\sqrt{3\left({a}^{2}+{b}^{2}+{c}^{2}\right)}}\)
Given a funcition $f(x)$, the derivative of $f$ with respect to $x$ can be found from first
principles using:\\
\[\frac{df}{dx}=\lim_{\Delta x \to 0}\frac{f(x+\Delta x)-f(x)}{\Delta x}\]