Rumusan Fungsi f(x) turunan yang terbentuk dari perkalian fungsi u(x) dan v(x), adalah:
![=\lim\limits_{h\to0}\frac{[u(x+h)v(x+h)-u(x+h)v(x)]+[u(x+h)v(x)-u(x)v(x)]}{h}](https://s0.wp.com/latex.php?latex=%3D%5Clim%5Climits_%7Bh%5Cto0%7D%5Cfrac%7B%5Bu%28x%2Bh%29v%28x%2Bh%29-u%28x%2Bh%29v%28x%29%5D%2B%5Bu%28x%2Bh%29v%28x%29-u%28x%29v%28x%29%5D%7D%7Bh%7D&bg=f9f9f9&fg=000000&s=0 "=\lim\limits_{h\to0}\frac{[u(x+h)v(x+h)-u(x+h)v(x)]+[u(x+h)v(x)-u(x)v(x)]}{h}")
![= \lim \limits_{h\to0}\frac{u(x+h)[v(x+h)-v(x)]}{h}+\lim \limits_{h\to0}\frac{[u(x+h)-u(x)]v(x)}{h}](https://s0.wp.com/latex.php?latex=%3D+%5Clim+%5Climits_%7Bh%5Cto0%7D%5Cfrac%7Bu%28x%2Bh%29%5Bv%28x%2Bh%29-v%28x%29%5D%7D%7Bh%7D%2B%5Clim+%5Climits_%7Bh%5Cto0%7D%5Cfrac%7B%5Bu%28x%2Bh%29-u%28x%29%5Dv%28x%29%7D%7Bh%7D&bg=f9f9f9&fg=000000&s=0 "= \lim \limits_{h\to0}\frac{u(x+h)[v(x+h)-v(x)]}{h}+\lim \limits_{h\to0}\frac{[u(x+h)-u(x)]v(x)}{h}")
Maka, rumus turunan fungsinya ialah:
contoh soal :
Tentukan turunan untuk f(x) = (x2 + 2x + 3)(4x + 5)
Pembahasan :
Misal :
u = (x2 + 2x + 3)
v = (4x + 5)
u = (x2 + 2x + 3)
v = (4x + 5)
maka
u ‘ = 2x + 2
v ‘ = 4
u ‘ = 2x + 2
v ‘ = 4
sehingga penerapan rumus di atas menjadi
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