Bab 9 Pembezaan

Posted on June 6, 2016 by user

9.2.3 Terbitan Pertama Fungsi Gubahan

(A) Membezakan fungsi gubahan dengan menggunakan Petua Rantai

Jika y = uⁿ

dengan keadaan udan v adalah fungsi dalam x

$\frac{d y}{d x} = \frac{d y}{d u} \times \frac{d u}{d x}$

Contoh 1:

Bezakan y = (x² – 1)⁸

Penyelesaian:

$\begin{array}{l} y = u^{8} katakan u = x^{2} - 1 \\ \frac{d y}{d u} = 8 u^{7} \frac{d u}{d x} = 2 x \\ \frac{d y}{d x} = \frac{d y}{d u} \times \frac{d u}{d x} \\ \frac{d y}{d x} = 8 u^{7} \times 2 x \\ \frac{d y}{d x} = 16 x u^{7} \\ \frac{d y}{d x} = 16 x {(x^{2} - 1)}^{7} \end{array}$

(B) Membezakan fungsi gubahan dengan menggunakan Kaedah Alternatif - Versi Mudah

Contoh:

Bezakan y = (x² – 1)⁸

Penyelesaian:

$\begin{array}{l} y = {(x^{2} - 1)}^{8} \\ \frac{d y}{d x} = 8 {(x^{2} - 1)}^{7} \frac{d}{d x} (x^{2} - 1) \\ \frac{d y}{d x} = 8 {(x^{2} - 1)}^{7} (2 x) \\ \frac{d y}{d x} = 16 x {(x^{2} - 1)}^{7} \end{array}$

Contoh 2:

$Diberi y = \frac{1}{3 x - 7}, cari \frac{d y}{d x}$

Penyelesaian

$\begin{array}{l} y = \frac{1}{3 x - 7} = {(3 x - 7)}^{- 1} \\ \frac{d y}{d x} = - 1 {(3 x - 7)}^{- 2} .3 \\ \frac{d y}{d x} = \frac{- 3}{{(3 x - 7)}^{2}} \end{array}$

Contoh 3:

$Diberi y = \sqrt{2 x^{2} - 5 x + 1}, cari \frac{d y}{d x}$

Penyelesaian

$\begin{array}{l} y = \sqrt{2 x^{2} - 5 x + 1} = {(2 x^{2} - 5 x + 1)}^{\frac{1}{2}} \\ \frac{d y}{d x} = \frac{1}{2} {(2 x^{2} - 5 x + 1)}^{- \frac{1}{2}} (4 x - 5) \\ \frac{d y}{d x} = \frac{4 x - 5}{2 \sqrt{2 x^{2} - 5 x + 1}} \end{array}$