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Nilai Turunan Pertama f’(π/2)

Diketahui f(x) = cos (x – π/2) sin2 3x, nilai f’(π/2) adalah …

A. 7

B. 5

C. 0

D. -1

E. -2

 

PEMBAHASAN

f(x) = cos (x – π/2) sin2 3x

misalkan:

u = cos (x – π/2)

v = sin2 3x

maka, f(x) = u . v

sehingga, f’(x) = u’v + v’u

 

mencari u’ dan v’

u’ = -sin (x – π/2)

v’ = 2 . 3 sin 3x . cos 3x

v’ = 6 sin 3x . cos 3x

 

f’(x) = u’v + v’u

f’(x) = -sin (x – π/2) . sin2 3x + 6 sin 3x . cos 3x . cos (x – π/2)

f’(π/2) = -sin (π/2 – π/2) . sin2 3π/2 + 6 sin 3π/2 . cos 3π/2 . cos (π/2 – π/2)

f’(π/2) = (0) (-1)2 + 6 (-1) (0) (0)

f’(π/2) = 0 (C)

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