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#