y=cos^3(12theta)

Question

find derivative using chain rule

Answer 1

y = x^3

x = cos(z)

z = 12 teta

dy/dtheta =

(dy/dz) (dz/dtheta) =

(dy/dx) (dx/dz) (dz/dtheta) =

3 x^2 [-sin(z)] 12 =

-36 cos^2(z) sin(z) =

-36 cos^2(12 theta) sin(12 theta)