How do you find the derivative of 1/(1+x^2)? Calculus Basic Differentiation Rules Quotient Rule 1 Answer Guilherme N. Jun 7, 2015 Renaming u=1+x^2, we can use the chain rule, which states that (dy)/(dx)=(dy)/(du)(du)/(dx) Also, we can rewrite 1/u as u^-1, following the rule of negative exponentials: a^-n=1/a^n (dy)/(dx)=-u^-2(2x) Substituting u: (dy)/(dx)=-(1+x^2)^2(2x)=-(2x)/(1+x^2)^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)? How do you use the quotient rule to differentiate y=cos(x)/ln(x)? How do you use the quotient rule to find the derivative of y=tan(x) ? How do you use the quotient rule to find the derivative of y=x/(x^2+1) ? How do you use the quotient rule to find the derivative of y=(e^x+1)/(e^x-1) ? How do you use the quotient rule to find the derivative of y=(x-sqrt(x))/(x^(1/3)) ? How do you use the quotient rule to find the derivative of y=x/(3+e^x) ? See all questions in Quotient Rule Impact of this question 1491 views around the world You can reuse this answer Creative Commons License