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

##### 1 Answer

Dec 13, 2016

# d/dx (x)/(x^2+1) = ( 1-x^2 ) / (x^2+1)^2#

#### Explanation:

If you are studying maths, then you should learn the Quotient Rule for Differentiation, and practice how to use it:

# d/dx(u/v) = (v(du)/dx-u(dv)/dx)/v^2 # , or less formally,# " "(u/v)' = (v(du)-u(dv))/v^2 #

I was taught to remember the rule in word; " *vdu minus udv all over v squared* ". To help with the ordering I was taught to remember the acronym, VDU as in Visual Display Unit.

So with

# :. d/dx(u/v) = (v(du)/dx-u(dv)/dx)/v^2 #

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

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

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