Page 73 - Modul problem posing berorientasi stem
P. 73
b. Aturan fungsi pangkat.
Jika ( ) = , n = bilangan bulat positif maka ′( ) =
Bukti.
( + ℎ) − ( ) ( + ℎ) −
′( ) = =
→ ℎ → ℎ
ℎ
ℎ ( − 1)
+ + +. . . . + ℎ + ℎ −
= 1! 2!
→ ℎ
( )
( .... )
= ! !
→
( )
= ( + +. . . . + ℎ + ℎ )
→ ! !
=
c. Aturan perkalian dengan konstanta
Jika ( )( ) = ( ) maka ( )′( ) = ′( )
Contoh 4.4.
Jika f(x) = 3 sinx maka ′( ) = 3
d. Aturan Jumlah dan Selisih
Jika ( ± )( ) = ( ) ± ( ) maka ( ± )′( ) = ′( ) ± ′( )
Contoh 4.5.
Jika f(x) = 2sinx + x - cos x maka ′( ) = 2 + 3 +
3
e. Aturan Hasil Kali
Jika ( . )( ) = ( ). ( ) maka ( . )′( ) = ′( ). ( ) + ( ). ′( )
Bukti
( + ℎ). ( + ℎ) − ( ). ( )
( . )′( ) =
→ ℎ
( + ℎ). ( + ℎ) − ( ) ( + ℎ) + ( ) ( + ℎ) − ( ). ( )
=
→ ℎ
= ( + ℎ) ( ) ( ) + ( ) ( ) ( )
→ →
= ( + ℎ) ( ) ( ) + ( ) ( ) ( )
→ → →
= ( ). ′( ) + ( ). ′( )
= ′( ). ( ) + ( ). ′( ) atau ( . )′ = ′ + ′
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