Question

Matematika:Diferensial
Tentukan turunan fungsi-fungsi berikut:
No.6-8

Answer 1

Nomor 6.
Dengan dalil rantai.


Nomor 7.
Akan terasa panjang.
F(x) = g(x)h(x)
Dengan,
g(x) = 2x²cos²(3x)
Maka, dengan aturan turunan perkalian:
g'(x) = 4x.cos²(3x) + 2x².2.cos(3x)[cos(3x)']
g'(x) = 4x.cos²(3x) + 4x².cos(3x)(-3sin(3x))
g'(x) = 4x.cos²(3x) - 12x².sin(3x)cos(3x)

Dan,
h(x) = sin x
h'(x) = cos x

Maka,
F'(x) = g'(x)h(x) + g(x)h'(x)
F'(x) = [4x.cos²(3x) - 12x².sin(3x)cos(3x)].sin x + 2x²cos²(3x).cos(x)
F'(x) = 4x.sin(x).cos²(3x) - 12x².sin(3x).sin(x).cos(3x) + 2x²cos²(3x).cos(x)

Nomor 8.
F(x) = 4x².sin²(2x).cos(x)
g(x) = 4x².sin²(2x)
h(x) = cos x, maka h' = -sin x
Maka,
g'(x) = 8x.sin²(2x) + 4x².(2.sin(2x).cos(2x))[2x]'
g'(x) = 8x.sin²(2x) + 8x²,sin(2x)cos(2x).2
g'(x) = 8x.sin²(2x) + 16x².sin(2x)cos(2x)
Maka,
F'(x) = g'(x)h(x) + g(x)h'(x)
F'(x) = [8x.sin²(2x)+16x².sin(2x)cos(2x)]cos x + 4x².sin²(2x).(-sin(x))
F'(x) = 8x.sin²(2x)cos(x)+16x².sin(2x)cos(2x)cos(x)-4x².sin²(2x)sin(x)