How do you find the derivative of #(cosx)(sinx)#? Calculus Basic Differentiation Rules Chain Rule 1 Answer Jim H Nov 21, 2016 Use #sin(2a) = 2sinAcosA# to rewrite. Explanation: #y = cosx sinx = 1/2 sin(2x)# #y' = 1/2 [cos(2x) * d/dx(2x)] = 1/2 cos(2x)*2 = cos(2x)# 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 3508 views around the world You can reuse this answer Creative Commons License