If y=sinxcosx, then at x=pi/3, dy/dx=

include the steps to solve this problem.

The answer is - 

Given: y = sin(x) cos(x)

Applying the product rule of differentiation, we get,

= sin(x) .  cos(x) + cos(x) sin(x)

                                   = sin(x) × -sin(x) + cos(x)cos(x)
 
                                   = - sin²x + cos²x
       
                                   = - sin²x + (1- sin²x)
                       
                                  = 1 - 2sin²x = cos 2x

Now, we need to find, 
 
= cos (2×60) = cos (120)

⇒

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