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)
Post a Comment for "Nilai Turunan Pertama f’(π/2) "