Misalkan f(x)= sin(cos2x), maka f'(x)=

f'(x)=d/dx (cos²x) cos(cos²x)
f'(x)=(2 cos) d/dx cosx cos (cos²x)
f'(x)=2 cos(cos²x)cosx(-sin x)
f'(x)=2 cos(cos²x)(-sin x) cosx
f'(x)=-2 sinx cosx cos(cos²x) atau -sin2x cos (cos²x)
 
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Turunan Fungsi Trigonometri.
Kelompok peminatan kelas XII kurikulum 2013 revisi 2016

f(x) = sin [u(x)] → f'(x) = cos [u(x)] u'(x)

f(x) = sin (cos² x)
f'(x) = cos (cos² x) [2 cos x (-sin x)]
       = -sin 2x cos (cos²x)
Jawaban: D.