Penjelasan dengan langkah-langkah:
Fungsi → turunan
[tex]f(x) = \frac{u}{v} \\ f'(x) = \frac{u' v - uv'}{{v}^{2} } [/tex]
Sehingga,
[tex]f(x) = \frac{3x - 1}{6x + 2} \\ u = 3x - 1 \\ u' = 3 \\ v = 6x + 2 \\ v' = 6 \\ \\ f'(x) = \frac{3(6x + 2) - 6(3x - 1)}{(6x + 2)^{2} } \\ f'(x) = \frac{18x + 6) - (18x - 6)}{36x^{2} + 24x + 4 } \\ f'(x) = \frac{12}{36x^{2} + 24x + 4 } \\ f'(x) = \frac{3}{9x^{2} + 6x + 1 } \\ f'(x) = \frac{3}{(3x + 1) ^{2} } [/tex]
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Penjelasan dengan langkah-langkah:
Fungsi → turunan
[tex]f(x) = \frac{u}{v} \\ f'(x) = \frac{u' v - uv'}{{v}^{2} } [/tex]
Sehingga,
[tex]f(x) = \frac{3x - 1}{6x + 2} \\ u = 3x - 1 \\ u' = 3 \\ v = 6x + 2 \\ v' = 6 \\ \\ f'(x) = \frac{3(6x + 2) - 6(3x - 1)}{(6x + 2)^{2} } \\ f'(x) = \frac{18x + 6) - (18x - 6)}{36x^{2} + 24x + 4 } \\ f'(x) = \frac{12}{36x^{2} + 24x + 4 } \\ f'(x) = \frac{3}{9x^{2} + 6x + 1 } \\ f'(x) = \frac{3}{(3x + 1) ^{2} } [/tex]