Question

evaluate dy/dx (2pi)/3) if y = 2 cot x - csc x.
a.-(10/3)
b. -(6/3)
c.-(8/3)
d.-(4/3)

Answer 1

dy/dx=-2/sin^2(x)+1/sin^2(x)*cos(x) and when you plug in x=2pi/3 you get dy/dx(2pi/3)=-2/(3/4)+1/(3/4)*(-1/2)=-8/3+4/3*(-1/2)=-8/3-2/3=-10/3