Diketahui f(x)=(x+7)/(5x-2)

Diketahui $f (x) = \frac{x + 7}{5 x - 2}, x \neq \frac{2}{5},$ maka $f^{'} (x) = \dots$

a. $\frac{2 x + 7}{5 x - 1}, x \neq \frac{1}{5}$

b. $\frac{5 x - 2}{x + 7}, x \neq - 7$

c. $\frac{7 x + 1}{- 2 x + 5}, x \neq \frac{5}{2}$

d. $\frac{x - 2}{5 x + 7}, x \neq - \frac{7}{5}$

e. $\frac{2 x - 7}{5 x + 1}, x \neq - \frac{1}{5}$

Penyelesaian

Diketahui:

$f (x) = \frac{x + 7}{5 x - 2}, x \neq \frac{2}{5}$

Ditanya: $f^{'} (x) = ?$

jawab

Misal $f (x) = y$

$y = \frac{x + 7}{5 x - 2}$

$y (5 x - 2) = x + 7$

$5 x y - 2 y = x + 7$

$5 x y - x = 2 y + 7$

$x (5 y - 1) = 2 y + 7$

$x = \frac{2 y + 7}{5 y - 1}$

$f^{'} (x) = \frac{2 x + 7}{5 x - 1}$

Cara Cepat

misal $f (x) = \frac{a x + b}{c x + d} \to f^{'} (x) = \frac{- d x + b}{c x - a}$

$f (x) = \frac{x + 7}{5 x - 2} \to f^{'} (x) = \frac{2 x + 7}{5 x - 1}$

Jawaban : a

Muda Berkarya Intelektual Normatif

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