Jikay = (x^3 + 2x^2 + 3x -1)/x, maka y' = . . . .

Jikay = (x^3 + 2x^2 + 3x -1)/x, maka y’ = . . . .

Jawaban Terkonfirmasi

$y' = 2x + 2 + frac{1}{ {x}^{2} }$

Pembahasan

$text{Turunan untuk fungsi} : : f(x) : : text{dinotasikan dengan} : : f'(x). : : text{Turunan fungsi} : : y : : text{dinotasikan dengan} : : y'. \ \$

Definisi Turunan

$boxed{y' = f'(x) = lim limits_{h to 0} frac{f(x + h) - f(x)}{h}} \ \$

Rumus turunan fungsi aljabar

$boxed{y = k cdot {x}^{n} : Rightarrow : y' = kn cdot {x}^{n - 1}} \ \$

Diketahui :

$y = frac{ {x}^{3} + 2 {x}^{2} + 3x - 1 }{x} \ \$

Ditanya :

$y' \ \$

Jawab :

Cara ❶.

$y = frac{ {x}^{3} + 2 {x}^{2} + 3x - 1 }{x} \ \ y = {x}^{2} + 2x + 3 - frac{1}{x} \ \ y' = 2x + 2 + 0 + frac{1}{ {x}^{2} } \ \ y' = 2x + 2 + frac{1}{ {x}^{2} } \ \$

Cara ❷.

$y = frac{ {x}^{3} + 2 {x}^{2} + 3x - 1 }{x} \ \ y = {x}^{2} + 2x + 3 - frac{1}{x} \ \ y' = lim limits_{h to 0} frac{f(x + h) - f(x)}{h} \ \ y' = lim limits_{h to 0} frac{ {(x + h)}^{2} + 2(x + h) + 3 - frac{1}{(x + h)} - ( {x}^{2} + 2x + 3 - frac{1}{x} ) }{h} \ \ y' = lim limits_{h to 0} frac{ {x}^{2} + 2xh + {h}^{2} + 2x + 2h + 3 - frac{1}{(x + h)} - ( {x}^{2} + 2x + 3 - frac{1}{x} ) }{h} \ \ y' = lim limits_{h to 0} frac{ 2xh + {h}^{2} + 2h - frac{1}{(x + h)} + frac{1}{x} }{h} \ \ y' = lim limits_{h to 0} frac{ 2xh + {h}^{2} + 2h + frac{1}{x} - frac{1}{(x + h)} }{h} \ \ y' = lim limits_{h to 0} frac{ 2xh + {h}^{2} + 2h + frac{h}{x(x + h)} }{h} \ \ y' = lim limits_{h to 0} left ( 2x + h + 2 + frac{1}{x(x + h)} right ) \ \ y' = 2x + 2 + frac{1}{ {x}^{2} } \ \$