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

Question

50048 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-31T16:57:08

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

Let $y=x/(1+x^2)$ .

We will use the following Quotient Rule for the Derivative :-

$y=(u(x))/(v(x)) rArr dy/dx={v(x)u'(x)-u(x)v'(x)}/(v(x))^2$

Hence,

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

$=[(1+x^2)(1)-(x){1'+(x^2)'}]/(1+x^2)^2$

$={(1+x^2)-x(0+2x)}/(1+x^2)^2$

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

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

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