How do you differentiate f(x)= x/(x^2+1)f(x)=xx2+1? Calculus Basic Differentiation Rules Quotient Rule 1 Answer Raknos Oct 1, 2017 {1-x^2}/(1+x^2)^21−x2(1+x2)2 Explanation: ={(1+x^2)d/dx (x) - x d/dx (x^2+1)}/(1+x^2)^2=(1+x2)ddx(x)−xddx(x2+1)(1+x2)2 ={1+x^2-x(2x)}/(1+x^2)^2=1+x2−x(2x)(1+x2)2 ={1-x^2}/(1+x^2)^2=1−x2(1+x2)2 Answer link Related questions What is the Quotient Rule for derivatives? How do I use the quotient rule to find the derivative? How do you prove the quotient rule? How do you use the quotient rule to differentiate y=(2x^4-3x)/(4x-1)y=2x4−3x4x−1? How do you use the quotient rule to differentiate y=cos(x)/ln(x)y=cos(x)ln(x)? How do you use the quotient rule to find the derivative of y=tan(x)y=tan(x) ? How do you use the quotient rule to find the derivative of y=x/(x^2+1)y=xx2+1 ? How do you use the quotient rule to find the derivative of y=(e^x+1)/(e^x-1)y=ex+1ex−1 ? How do you use the quotient rule to find the derivative of y=(x-sqrt(x))/(x^(1/3))y=x−√xx13 ? How do you use the quotient rule to find the derivative of y=x/(3+e^x)y=x3+ex ? See all questions in Quotient Rule Impact of this question 1639 views around the world You can reuse this answer Creative Commons License