f(x)= cos^3 (1/x^3) , f'(x)= ?

Turunan dengan substitusi

f(x)= cos³ (1/x³)
y = cos³ (1/x³)
misalkan :
u = 1/x³ = x⁻³ --> du/dx = -3x⁻⁴
t = cos u --> dt/du  = - sin u
y = t³ --> dy/dt = 3t²

y' = dy/dx
dy/dx  = dy/dt . dt/du. du/dx
y' = 3t² . (-sin u) . (- 3x⁻⁴)
y' =  9x⁻⁴ (t²)(sin u)
y' = 9 x⁻⁴(cos u)² (sin 1/x³)
y'  = (9/ x⁴)  cos² (1/x³)  sin (1/x³)