What is the derivative of $(\frac{x}{x^{2} + 1})$ $(x/(x^2+1))$ ?

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Answer 1 · 2015-06-04T13:13:41

Using quotient rule, which states that for $y = \frac{f (x)}{g (x)}$ $y=f(x)/g(x)$ ,

$y'=(f'(x)g(x)-f(x)g'(x))/(g(x))^2$ ,

We can proceed to derivate this with no big problems.

$(dy)/(dx)=(1*(x^2+1)-x*2x)/(x^2+1)^2$

$(dy)/(dx)=(x^2+1-2x^2)/(x^2+1)^2$

$color(green)((dy)/(dx)=(-x^2+1)/(x^2+1)^2)$

What is the derivative of (x/(x^2+1))(xx2+1)(x/(x^2+1))?