Diberikan f® = 2r^2/3 - 2r^1/2. Nilai f'(1) = . . .

Diberikan f® = 2r^2/3 – 2r^1/2. Nilai f'(1) = . . .

Jawaban Terkonfirmasi

$boxed{f'(1) = frac{1}{3}} \$

Pembahasan

$text{Turunan fungsi f(x) dinotasikan dengan} : : f'(x) : : text{atau} : : frac{df(x)}{dx} \ \$

Definisi Turunan

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

Rumus-rumus turunan fungsi aljabar

$f(x) = k cdot {(ax + b)}^{n} : Rightarrow : f'(x) = k cdot a cdot n cdot {(ax + b)}^{n - 1} \ \ f(x) = k {x}^{n} : Rightarrow : f'(x) = k cdot n cdot {x}^{n - 1} \ \$

Diketahui :

$f(r) = 2 {r}^{ frac{2}{3} } - 2 {r}^{ frac{1}{2} } \ \$

Ditanya :

$f'(1) \ \$

Jawab :

$f(r) = 2 {r}^{ frac{2}{3} } - 2 {r}^{ frac{1}{2} } \ \ f(r) = 2 left ( {r}^{ frac{2}{3} } - {r}^{ frac{1}{2} } right ) \ \ f'(r) = 2 cdot frac{2}{3} cdot {r}^{( frac{2}{3} - 1) } - 2 cdot frac{1}{2} cdot {r}^{( frac{1}{2} - 1) } \ \ f'(r) = frac{4}{3} cdot {r}^{ - frac{1}{3} } - {r}^{ - frac{1}{2} } \ \ f'(r) = frac{4}{3 sqrt[3]{r} } - frac{1}{ sqrt{r} } \ \ f'(1) = frac{4}{3 sqrt[3]{1} } - frac{1}{ sqrt{1} } \ \ f'(1) = frac{4}{3} - 1 \ \ f'(1) = frac{4}{3} - frac{3}{3} \ \ f'(1) = frac{4 - 3}{3} \ \ boxed{f'(1) = frac{1}{3}} \ \$