How do you use the chain rule to differentiate #f(x) = cos(lnx)#? Calculus Basic Differentiation Rules Chain Rule 1 Answer Noah G Aug 2, 2016 Let #y = cosu# and #u = lnx#. Then #y' = -sinu# and #u' = 1/x# #f'(x) = -sinu xx 1/x = -sin(lnx) xx 1/x = -(sin(lnx))/x# Hopefully this helps! 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 7802 views around the world You can reuse this answer Creative Commons License