[tex]\bf{f\left(x\right)=\frac{10x^{2}-2x}{x-1}}[/tex] [tex]\bf{maka\ f'\left(x\right)=?}[/tex] Teri.... Question from @Sinogen

Jawaban:

$\frac{10 {x}^{2} - 20x + 2 }{{x}^{2} - 2x + 1}$

Penjelasan dengan langkah-langkah:

$\frac{d}{dx} ( \frac{u}{v} ) = \frac{ \frac{d}{dx} u(v) - u( \frac{d}{dx} v)}{ {v}^{2} } \\ = \frac{ \frac{d}{dx} (10 {x}^{2} - 2x)(x - 1) - (10 {x}^{2} - 2x) \frac{d}{dx} (x - 1)}{(x - 1) {}^{2} } \\ = \frac{(20x - 2)(x - 1) - (10 {x}^{2} - 2x)(1) }{ {x}^{2} - 2x + 1} \\ = \frac{20 {x}^{2} - 22x + 2 - 10 {x}^{2} + 2x }{ {x}^{2} - 2x + 1} \\ = \frac{10 {x}^{2} - 20x + 2 }{{x}^{2} - 2x + 1}$

Sinogen A+ :D

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KellDSini

Penjelasan dengan langkah-langkah:

Pembahasan

Diketahui :

fungsi f(x) = 10x² - 2x/x - 1

Ditanya :

f'(x)?

Dijawab :

Misal :

u = 10x² - 2x

u' = 2 . 10x²-¹ - 1 . 2x¹-¹

u' = 20x¹ - 2x⁰

u' = 20x - 2

v = x - 1

v = 1x - 1

v' = 1 . 1x¹-¹ - 0

v' = 1x⁰

v' = 1

Maka

f(x) = 10x² - 2x/x - 1

f'(x) = u'v - uv'/v²

f'(x) = (20x-2)(x-1)-(10x²-2x)(1)/(x-1)²

f'(x) = (20x(x-1)-2(x-1)-(10x²-2x)(1)/(x-1)(x-1)

f'(x) = (20x²-20x-2x+2)-(10x²-2x)/(x(x-1)-1(x-1)

f'(x) = (20x²-22x+2)-(10x²-2x)/x²-x-x+1

f'(x) = 20x²-22x+2-10x²+2x/x²-2x+1

f'(x) = 20x²-10x²-22x+2x+2/x²-2x+1

f'(x) = 10x²-20x+2/x²-2x+1

Kesimpulan

Turunan pertama dari fungsi f(x) = 10x² - 2x/x - 1 adalah f'(x) = 10x² - 20x + 2/x² - 2x + 1

Detail jawaban

Mapel : Matematika

Kelas : XI(11)

Materi : Bab 9 - Turunan fungsi aljabar

Kode kategorisasi : 11.2.9

Kata kunci : turunan fungsi, turunan pertama

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