Question

$$D(\frac{x^{a}}{x^{-b}})^{a-b}\times(\frac{x^{b}}{x^{c}})^{b+c}\times(\frac{x^{-a}}{x^{-c}})^{c+a}$$

Evaluate

$D\left(x^{a+b}\right)^{a-b}\left(x^{b-c}\right)^{b+c}\left(x^{c-a}\right)^{a+c}$

Differentiate w.r.t. x

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