How do you find the derivative of #x/(1+x^2)#?

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Answer 1 · 2016-01-08T20:11:34

#(1-x^2)/(1+x^2)^2#

Use the quotient rule, which states that for a function

#f(x)=(g(x))/(h(x))#

the derivative of the function is

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

Thus, the derivative of #x/(1+x^2)# is

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

Find each derivative.

#d/dx(x)=1#

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

Hence the derivative is equal to

#((1+x^2)-x(2x))/(1+x^2)^2#

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