Differentiate this quotient and find the slope? Am I making an error? I have this equation that I want to differentiate:
$$y = \frac{2x}{x^2+1}$$
and so I think $y' =$ (using quotient rule)
$$= \frac{(x^2+1)*2 - 2x(2x)}{(x^2+1)^2}$$
$$=\frac{2x^2 + 2 - 4x^2}{(x^2 + 1)^2}$$
$$=\frac{-2x^2 + 2}{(x^2 + 1)^2}$$
$$= \frac{-2(x^2-1)}{(x^2+1)^2}$$
Is that right? Am I making a mistake? I want to find the slope at x = 1 and so given my differential, the slope is = 0 right?

Perfect! I have checked your work and it is flawless. You have explained every step in detail and made it completely clear. 
