O slideshow foi denunciado.
Utilizamos seu perfil e dados de atividades no LinkedIn para personalizar e exibir anúncios mais relevantes. Altere suas preferências de anúncios quando desejar.
Diferensiasi
fungsi sederhana
Kaidah- kaidah Deferensiasi
• Jika Y=K, dimana K adalah konstanta,
maka Y’ =
• Misal Y = 4
0=
dx
dy
0=
dx
dy
• Jika Y = xn
• Dimana n adalah konstanta maka
Y’ = . Xn-1
n
dx
dy
=
Cara 1
Misal
Y = (x² - 5x )²
= x4
+ 10 x3
+ 25 x2
= 4x3
+ 30 x2
+ 50 x
dx
dy
Cara 2
Y = (x² + 5x ) (x² + 5x )
Misal
U = x² + 5x U’ = 2x + 5
V = x² + 5x V’ = 2x + 5
= UV’ + VU’
= (x² + 5x ) (2x + 5 ) ...
Cara 3
Y = (x² + 5x )²
u = x² + 5x u’ = 2x + 5
n = 2
= 2(x² + 5x ) (2x + 5)
= (2x2
+ 10 x) (2x + 5)
= 4x3
+ 10 x2
+ 20 x2
...
Diferensiasi penjumlahan ( pengurangan ) fungsi
Jika Y = u ± v
Maka = ± = u’ + v’
Misal Y= 4x² + x3
u = 4x² u’ = 8x
v = x3...
Diferensiasi perkalian fungsi
Jika Y = u . v
Maka = u . v’ + v . u’
Misal Y= 4x² . x3
u = 4x² u’ = 8x
v = x3
v’ = 3x²
= 4x...
Diferensiasi pembagian fungsi
Jika Y =
Maka =
Misal Y=
u = x² + 1 u’ = 2x
v = x + 2 v’ = 1
v
u
dx
dy
2
'.'.
v
vuuv −
2
12
...
=
=
=
dx
dy
2
2
)2(
1.1)2)(2(
+
+−+
x
xxx
44
142
2
22
++
−−+
xx
xxx
44
14
2
2
++
−+
xx
xx
Hitunglah dari fungsi- fungsi sbb :
1. Y =
2. Y = 3 x4
+ (2x – 1)²
3. Y =
4. Y = (x² - 4) ( 2x – 6 )
5. Y = 2x3
– 4x² + 7x...
6. Y =
7. Y = (x²+2) 3
8. Y = 5x²
9. Y = 2x² + 4x + 1
10. Y = -5 + 3x - - 7x3
5
222
−
+−
x
xx
x²
2
3
Próximos SlideShares
Carregando em…5
×

Matematika Ekonomi Diferensiasi fungsi sederhana

8.524 visualizações

Publicada em

matematika ekonomi bab diferensiasi fungsi sederhana

Publicada em: Economia e finanças
  • Seja o primeiro a comentar

Matematika Ekonomi Diferensiasi fungsi sederhana

  1. 1. Diferensiasi fungsi sederhana
  2. 2. Kaidah- kaidah Deferensiasi • Jika Y=K, dimana K adalah konstanta, maka Y’ = • Misal Y = 4 0= dx dy 0= dx dy
  3. 3. • Jika Y = xn • Dimana n adalah konstanta maka Y’ = . Xn-1 n dx dy =
  4. 4. Cara 1 Misal Y = (x² - 5x )² = x4 + 10 x3 + 25 x2 = 4x3 + 30 x2 + 50 x dx dy
  5. 5. Cara 2 Y = (x² + 5x ) (x² + 5x ) Misal U = x² + 5x U’ = 2x + 5 V = x² + 5x V’ = 2x + 5 = UV’ + VU’ = (x² + 5x ) (2x + 5 ) + (x² + 5x ) (2x + 5 ) = 2x3 + 5 x2 + 10 x2 + 25x + 2x3 + 5 x2 + 10 x2 + 25x = 4x3 + 30 x2 + 50x dx dy
  6. 6. Cara 3 Y = (x² + 5x )² u = x² + 5x u’ = 2x + 5 n = 2 = 2(x² + 5x ) (2x + 5) = (2x2 + 10 x) (2x + 5) = 4x3 + 10 x2 + 20 x2 + 50x = 4x3 + 30x2 + 50x dx dy
  7. 7. Diferensiasi penjumlahan ( pengurangan ) fungsi Jika Y = u ± v Maka = ± = u’ + v’ Misal Y= 4x² + x3 u = 4x² u’ = 8x v = x3 v’ = 3x² = 8x + 3x² dx du dx dy dx dv dx dy
  8. 8. Diferensiasi perkalian fungsi Jika Y = u . v Maka = u . v’ + v . u’ Misal Y= 4x² . x3 u = 4x² u’ = 8x v = x3 v’ = 3x² = 4x² . 3x² + x3 . 8x = 12 x4 + 8x4 = 20 x4 dx dy dx dy
  9. 9. Diferensiasi pembagian fungsi Jika Y = Maka = Misal Y= u = x² + 1 u’ = 2x v = x + 2 v’ = 1 v u dx dy 2 '.'. v vuuv − 2 12 + + x x
  10. 10. = = = dx dy 2 2 )2( 1.1)2)(2( + +−+ x xxx 44 142 2 22 ++ −−+ xx xxx 44 14 2 2 ++ −+ xx xx
  11. 11. Hitunglah dari fungsi- fungsi sbb : 1. Y = 2. Y = 3 x4 + (2x – 1)² 3. Y = 4. Y = (x² - 4) ( 2x – 6 ) 5. Y = 2x3 – 4x² + 7x - 5 2 1 x x 1 dx dy
  12. 12. 6. Y = 7. Y = (x²+2) 3 8. Y = 5x² 9. Y = 2x² + 4x + 1 10. Y = -5 + 3x - - 7x3 5 222 − +− x xx x² 2 3

×