How do you find the derivative of #f(x)=ln(3x^(2)+6x+5)#? Calculus Basic Differentiation Rules Chain Rule 1 Answer Eddie Jun 24, 2016 #(6(x+1))/(3x^(2)+6x+5)# Explanation: #f(x)=ln(3x^(2)+6x+5)# as a general matter if #y = ln ( f(x) )# then #y' = 1/(f(x)) f'(x)# [chain rule] here #f'(x)=1/(3x^(2)+6x+5)(3x^(2)+6x+5)'# #=(6x+6)/(3x^(2)+6x+5)# 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 2593 views around the world You can reuse this answer Creative Commons License