Tentukan turunan dari y=cos(cos(cos 2x))

subtitusi :

2x = a  , cos a = b , cos b = c

maka y jadi :

y = cos c

dy = d(cos c)

     = -sin c . dc <= c = cos b

   = -sin(cos b) . d(cos b)

  = sin(cos b).sin b . db  <= b = cos a

 = sin(cos(cos a)).sin(cos a).d(cos a)

 = – sin(cos(cos a)).sin(cos a).sin a . da <= a = 2x

 = – sin(cos(cos (2x))).sin(cos (2x)).sin(2x) . d(2x)

dy/dx = -2.sin(cos(cos (2x))).sin(cos (2x)).sin(2x) <= sin 2x bisa diubah

          = -4.sin(cos(cos (2x))).sin(cos (2x)).sin x.cos x

Gunakan aturan rantai.

Misal, a = 2x

maka, da/dx = 2

Misal, b = cos(a)

maka da/db = -sin(a)

Misal, c = cos(b)

maka, dc/db = -sin(b)

Misal, y = cos(c)

maka, dy/dc = -sin(c)

Maka, dy/dx = dy/dc . dc/db . da/db . da/dx

= (-sin(c))(-sin(b))(-sin(a))(2)

= -2sin(c).sin(b).sin(a)

= -2.sin(cos(b)).sin(b).sin(a)

= -2.sin(cos(cos(a))).sin(cos(a)).sin(a)

= -2.sin(cos(cos(2x))).sin(cos(2x)).sin(2x)