$$(\frac{x^{a}}{x^{b}})^{a+b}(\frac{x^{b}}{x^{c}})^{b+c}(\frac{x^{c}}{x^{a}})^{c+a}$$
$\left(a^{2}-b^{2}\right)x^{a-b-1}\left(x^{a-b}\right)^{a+b-1}\left(x^{b-c}\right)^{b+c}\left(x^{c-a}\right)^{a+c}+\left(b^{2}-c^{2}\right)x^{b-c-1}\left(x^{a-b}\right)^{a+b}\left(x^{b-c}\right)^{b+c-1}\left(x^{c-a}\right)^{a+c}+\left(c^{2}-a^{2}\right)x^{c-a-1}\left(x^{a-b}\right)^{a+b}\left(x^{b-c}\right)^{b+c}\left(x^{c-a}\right)^{a+c-1}$
