How do you find the derivative of sqrt((x^2-1) / (x^2+1))? Calculus Basic Differentiation Rules Chain Rule 1 Answer Konstantinos Michailidis Sep 12, 2015 It is f'(x)=(2x)/((sqrt(x^2-1))*(x^2+1)^(3/2)) Explanation: We have that f(x)=sqrt((x^2-1)/(x^2+1)) hence f'(x)=1/2*1/(sqrt((x^2-1)/(x^2+1)))*((x^2-1)/(x^2+1))' f'(x)=1/2*sqrt(x^2+1)/sqrt(x^2-1)*((2x(x^2+1)-(x^2-1)2x)/(x^2+1)) f'(x)=1/2*sqrt(x^2+1)/sqrt(x^2-1)*(4x/(x^2+1)^2) f'(x)=(2x)/((sqrt(x^2-1))*(x^2+1)^(3/2)) Answer link Related questions What is the Chain Rule for derivatives? How do you find the derivative of y= 6cos(x^2) ? How do you find the derivative of y=6 cos(x^3+3) ? How do you find the derivative of y=e^(x^2) ? How do you find the derivative of y=ln(sin(x)) ? How do you find the derivative of y=ln(e^x+3) ? How do you find the derivative of y=tan(5x) ? How do you find the derivative of y= (4x-x^2)^10 ? How do you find the derivative of y= (x^2+3x+5)^(1/4) ? How do you find the derivative of y= ((1+x)/(1-x))^3 ? See all questions in Chain Rule Impact of this question 1798 views around the world You can reuse this answer Creative Commons License