How do you find the derivative of # f(x)= (1/2) sin(2x) + cos(x) #? Calculus Basic Differentiation Rules Chain Rule 1 Answer Ratnaker Mehta Jun 14, 2016 #f'(x)=cos2x-sinx.# Explanation: Given that #f(x)=(1/2)sin2x+cosx.# #:. f'(x)=(1/2)(sin2x)'+(cosx)'# #:. f'(x)=(1/2)(cos2x)(2x)'+(-sinx)= (1/2)(2)cos2x-sinx=cos2x-sinx.# 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 1135 views around the world You can reuse this answer Creative Commons License