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Aturan Dasar Turunan Fungsi Aljabar

Turunan dari fungsi kontinu y = f(x) merupakan laju perubahan nilai y terhadap nilai x.
Jika perubahan nilai x tersebut sebesar h, maka kita dapat menuliskan :
sebagai hasil dari perubahan tersebut (seperti gambar dibawah ini).
Jika nilai h diambil kecil mendekati nol (limit h mendekati nol), maka perubahan tersebut akan menjadi laju perubahan. Inilah yang menjadi dasar dari konsep turunan.
Sehingga turunan dari fungsi f(x) dilambangkan dengan f �(x) didefinisikan sebaagai
Jadi notasi turunan dari fungsi y = f(x) dapat ditulis sebagai

Untuk lebih jelasnya ikutilah contoh soal berikut ini:

01. Dengan menggunakan definisi turunan, tentukanlah turunan dari setiap fungsi berikut ini :
(a) f(x) = 3x � 5
(b) f(x) = 4x2 + 3x
(c) f(x) = x3 � 2x
Jawab
(a) f(x) = 3x � 5

(b) f(x) = 4x2 + 3x

(c) f(x) = x3 � 2x

Berdasarkan definisi turunan di atas, kita dapat memperoleh aturan tersendiri untuk mendapatkan rumus dasar turunan fungsi aljabar, yakni:
Jika f(x) = axn maka f �(x) = n.axn-1

Pengembangan dari rumus tersebut adalah turunan bentuk f(x) = ax dan bentuk f(x) = c (dimana c suatu konstanta), yakni sebagai berikut :
Jika f(x) = ax maka f �(x) = a
Jika f(x) = a maka f �(x) = 0

Untuk lebih jelasnya ikutilah contoh soal berikut ini:

02. Dengan menggunakan rumus dasar turunan, tentukanlah turunan pertama dari setiap fungsi berikut ini :
 

03. Dengan menggunakan rumus dasar turunan, tentukanlah turunan pertama dari setiap fungsi berikut ini:
 
 
 

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