How do you find the derivative of #sqrt (x^2 +1)#? Calculus Basic Differentiation Rules Chain Rule 1 Answer Alan N. Mar 10, 2016 #x/sqrt(x^2 + 1)# Explanation: #f(x) = sqrt(x^2 + 1)# #f(x) = (x^2 + 1)^(1/2)# #f'(x) = 1/2(x^2 + 1)^(-1/2) . (2x + 0)# #f'(x) = (2x)/(2 sqrt(x^2 + 1))# #f'(x) = x/sqrt(x^2 + 1)# 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 1047 views around the world You can reuse this answer Creative Commons License