How do you differentiate $f (x) = \frac{x}{x^{2} + 1}$ $f(x)= x/(x^2+1)$ ?

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Answer 1 · 2017-10-01T16:46:42

$\frac{1 - x^{2}}{{(1 + x^{2})}^{2}}$ ${1-x^2}/(1+x^2)^2$

$= \frac{(1 + x^{2}) \frac{d}{d x} (x) - x \frac{d}{d x} (x^{2} + 1)}{{(1 + x^{2})}^{2}}$ $={(1+x^2)d/dx (x) - x d/dx (x^2+1)}/(1+x^2)^2$

$= \frac{1 + x^{2} - x (2 x)}{{(1 + x^{2})}^{2}}$ $={1+x^2-x(2x)}/(1+x^2)^2$

$= \frac{1 - x^{2}}{{(1 + x^{2})}^{2}}$ $={1-x^2}/(1+x^2)^2$

How do you differentiate f(x)=xx2+1f(x)= x/(x^2+1)?