Question

Find d/dx(cos x-sin x) at x=2π/3

Answer 1

d/dx(cosx-sinx) = -sinx-cosx
at x=2π/3
-√3/2-(-1/2)
or
-√3/2+1/2

Answer 2

hello users .......

we have to find 
d/dx(cos x-sin x) at x=2π/3 =?

solution :- 
we know that :
d/dx (cos x) = -sin x
and 
d/dx (sin x) =  cos x 

here 
d/dx(cos x-sin x) = d/dx (cos x) - d/dx (sin x)
= -sin x - cos x 

 now at x=2π/3

d/dx(cos x-sin x) =  -sin x - cos x 
= -sin 2π/3 - cos 2π/3 
= -sin 120° -cos 120° 
= - sin (180 - 60) - cos (180 -60 )
= -sin 60 - ( -cos 60 )
= -sin 60° + cos 60°
= -√3/2 + 1/2  = (1-√3) /2 answer

⊕⊕hope it helps ⊕⊕