How do you differentiate #f(x)=sqrtcos(7-4x) # using the chain rule? Calculus Basic Differentiation Rules Chain Rule 1 Answer Bdub Mar 30, 2016 #f'(x)=(4sin(7-4x))/(2sqrt(cos(7-4x))# Explanation: #f(x)=sqrt(cos(7-4x))# #f(x)=(cos(7-4x))^(1/2)# #f'(x)=1/2 (cos(7-4x))^(-1/2) * -sin(7-4x) * -4# #f'(x)=(4sin(7-4x))/(2sqrt(cos(7-4x))# 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 1132 views around the world You can reuse this answer Creative Commons License