Find the value of (f o g)' at x = 4 when f(u)= cos(piu/24) and u=g(x)=6sqrt(x)

Answer 1

y = cos (6 pi x^.5/24) = cos ( pi x^.5/4)
let z = x^.5 then dz/dx = .5 x^-.5
y = cos( pi z/4)
dy/dz = -(pi/4)sin (pi z/4)
dy/dx = dy/dz * dz/dx
dy/dx = [-(pi/4)sin (pi x^.5 /4)] .5 x^-.5
if x = 4 then x^.5 = 2
dy/dx = [-pi/4 sin (pi/2) ] (1/4) = -pi/16