Diketahui $f(x)=\frac{x+7}{5x-2}, x \ne \frac{2}{5},$ maka $f'(x)=\dots$
a. $\frac{2x+7}{5x-1}, x \ne \frac{1}{5}$
b. $\frac{5x-2}{x+7}, x \ne -7 $
c. $\frac{7x+1}{-2x+5}, x\ne \frac{5}{2}$
d. $\frac{x-2}{5x+7}, x\ne -\frac{7}{5}$
e. $\frac{2x-7}{5x+1}, x\ne -\frac{1}{5}$
Penyelesaian
Diketahui:
$f(x)=\frac{x+7}{5x-2}, x \ne \frac{2}{5}$
Ditanya: $f'(x)=?$
jawab
Misal $f(x)=y$
$y=\frac{x+7}{5x-2}$
$y(5x-2)=x+7$
$5xy-2y=x+7$
$5xy-x=2y+7$
$x(5y-1)=2y+7$
$x=\frac{2y+7}{5y-1}$
$f'(x)=\frac{2x+7}{5x-1}$
Cara Cepat
misal $f(x)=\frac{ax+b}{cx+d}\to f'(x)=\frac {-dx+b}{cx-a}$
$f(x)=\frac{x+7}{5x-2} \to f'(x)=\frac{2x+7}{5x-1}$
Jawaban : a
Muda Berkarya Intelektual Normatif