A problem on finding dy/dx If $a+b+c=0$ and $$y=\frac{1}{x^b+x^{-c}+1}+\frac{1}{x^c+x^{-a}+1}+\frac{1}{x^a+x^{-b}+1}$$then $\frac{dy}{dx}$=?
The only way which I can think of solving this is by differentiating each term. However, is there a simpler way?

$$y=\frac{1}{x^b+x^{a+b}+1}+\frac{1}{x^{-a-b}+x^{-a}+1}+\frac{1}{x^a+x^{-b}+1}$$
$$y=\frac{1}{x^b+x^{a+b}+1}+\frac{x^{a+b}}{1+x^{b}+x^{a+b}}+\frac{x^b}{x^{a+b}+1+x^b}$$
