How do you differentiate # y = 3x cos (x/3) - sin (x/3)#? Calculus Differentiating Trigonometric Functions Differentiating sin(x) from First Principles 1 Answer James May 13, 2018 the answer #y'=[8cos(x/3)]/3-xsin(x/3)# Explanation: show below #y = 3x cos (x/3) - sin (x/3)# #y'=3[x*-1/3sin(x/3)+cos(x/3)*1]-1/3*cos(x/3)# #y'=-x*sin(x/3)+3cos(x/3)-1/3*cos(x/3)# #y'=[8cos(x/3)]/3-xsin(x/3)# Answer link Related questions How do you differentiate #f(x)=sin(x)# from first principles? What is the derivative of #y=3sin(x) - sin(3x)#? How do you find dy/dx if #x + tan(xy) = 0#? How do you find the derivative of the function #y=cos((1-e^(2x))/(1+e^(2x)))#? How do you differentiate #f(x)=2secx+(2e^x)(tanx)#? How do you find the derivate for #y = pisinx - 4cosx#? How do you find the derivative of #f(t) = t^2sin t#? What is the derivative of #sin^2(lnx)#? How do you compute the 200th derivative of #f(x)=sin(2x)#? How do you find the derivative of #sin(x^2+1)#? See all questions in Differentiating sin(x) from First Principles Impact of this question 4666 views around the world You can reuse this answer Creative Commons License