How do you use the quotient rule to find the derivative of $y=x/(x^2+1)$ ?

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Answer 1 · 2014-09-22T21:30:47

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

Make all of the necessary substitutions

$f(x)=x/(x^2+1)$

$g(x) = x$
$g'(x)= 1$

$h(x)=x^2+1$
$h'(x)=2x+0$
$h'(x)=2x$

$(h(x))^2=(x^2+1)^2$

$f'(x)=((x^2+1)*1-x*2x)/(x^2+1)^2$

$f'(x)=(x^2+1-2x^2)/(x^2+1)^2$

$f'(x)=(1-x^2)/(x^2+1)^2$

How do you use the quotient rule to find the derivative of y=x/(x^2+1)y=x/(x^2+1) ?