Bab 9 Pembezaan

Posted on June 9, 2020 by Myhometuition

Bab 9 Pembezaan

9.2.1 Terbitan Pertama untuk Fungsi Polinomial (Contoh)

Contoh:

Cari dy/dx bagi setiap fungsi yang berikut:

(a) y = 12

(b) y = x⁴

(c) y = 3x

(d) y = 5x³

\begin{array}{l} (e) y = \frac{1}{x} \\ (f) y = \frac{2}{x^{4}} \\ (g) y = \frac{2}{5 x^{2}} \\ (h) y = 3 \sqrt{x} \\ (i) y = 4 \sqrt{x^{3}} \end{array}

Penyelesaian:

(a) y = 12

dy/dx = 0

(b) y = x⁴

dy/dx = 4x³

(c) y = 3x

dy/dx = 3

(d) y = 5x³

dy/dx = 15x²

(e)

\begin{array}{l} y = \frac{1}{x} = x^{- 1} \\ \frac{d y}{d x} = - x^{- 1 - 1} = - \frac{1}{x^{2}} \end{array}

(f)

\begin{array}{l} y = \frac{2}{x^{4}} = 2 x^{- 4} \\ \frac{d y}{d x} = - 4 (2 x^{- 4 - 1}) \\ = - 8 x^{- 5} = - \frac{8}{x^{5}} \end{array}

(g)

\begin{array}{l} y = \frac{2}{5 x^{2}} = \frac{2 x^{- 2}}{5} \\ \frac{d y}{d x} = - 2 (\frac{2 x^{- 2 - 1}}{5}) \\ = - \frac{4 x^{- 3}}{5} \\ = - \frac{4}{5 x^{3}} \end{array}

(h)

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

(i)

\begin{array}{l} y = 4 \sqrt{x^{3}} = 4 {(x^{3})}^{\frac{1}{2}} = 4 x^{\frac{3}{2}} \\ \frac{d y}{d x} = \frac{3}{2} (4 x^{\frac{3}{2} - 1}) \\ = 6 x^{\frac{1}{2}} = 6 \sqrt{x} \end{array}