Question

mohon Bantuannya kak​

Answer 1

Verified answer

turunan fungsi

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Sifat turunan fungsi rasional

[tex]\boxed{\rm{y = \frac{f(x)}{g(x)} \leftrightarrow y' = \frac{f'(x) . g(x) - f(x) . g'(x)}{g^{2} (x)}} }[/tex]

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a)) turunan  dari [tex]\rm{y = \frac{2x - 1}{3x + 5}}[/tex]  :

misalkan u = 2x - 1 → u' = 2

               v = 3x + 5 → v' = 3

maka,

[tex]\rm{y' = \frac{u'v - uv'}{v^{2}}}[/tex]

[tex]\rm{y' = \frac{2(3x + 5) - 3(2x - 1)}{(3x + 5)^{2}}}[/tex]

[tex]\rm{y' = \frac{6x + 10 - 6x + 3}{9x^{2} + 30x + 25}}[/tex]

[tex]\rm{y' = \frac{13}{9x^{2} + 30x + 25}}[/tex]

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b)) turunan dari [tex]\rm{y = \frac{x + 1}{3x + 2}}[/tex] :

misalkan u = x + 1 → u' = 1

               v = 3x + 2 → v' = 3

maka,

[tex]\rm{y' = \frac{u'v - uv'}{v^{2}}}[/tex]

[tex]\rm{y' = \frac{1(3x + 2) - 3(x + 1)}{(3x + 2)^{2}}}[/tex]

[tex]\rm{y' = \frac{3x + 2 - 3x - 3}{(3x + 2)^{2}}}[/tex]

[tex]\rm{y' = -\frac{1}{(3x + 2)^{2}}}[/tex]

[tex]\rm{y' = -\frac{1}{9x^{2} + 12x + 4}}[/tex]

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