ditanyakan turunan fungsi f(x) adalah...
Turunan fungsi f(x) adalah [tex]\sf \dfrac{6 {x}^{2} + 4x - 9 }{ {(3x + 1)}^{2} }[/tex]
Pembahasan
[tex] \sf f(x) = \dfrac{ {2x}^{2} + 3}{3x + 1} [/tex]
Misal: • u = 2x² + 3 → u' = 4x
ㅤㅤㅤ• v = 3x + 1 → v' = 3
Penyelesaian:
[tex]\begin{aligned}\sf f'(x)&=\sf \frac{u'v - uv'}{ {v}^{2} } \\ \sf &=\sf \frac{4x \: (3x + 1) - (2 {x}^{2} + 3) \: 3 }{ {(3x + 1)}^{2} } \\ \sf &= \sf \frac{12 {x}^{2} + 4x - 6 {x}^{2} - 9 }{ {(3x + 1)}^{2} } \\ \sf &=\sf \frac{6 {x}^{2} + 4x - 9 }{ {(3x + 1)}^{2} } \end{aligned}[/tex]
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