# Turunan Bentuk Perkalian dan Pembagian

### Turunan Bentuk Perkalian dan Pembagian

###### Turunan Bentuk Perkalian

$$y = u \:.\: v \rightarrow y' = u' \:.\: v + u \:.\: v'$$

$$y = u \:.\: v \:.\: w \rightarrow y' = u' \:.\: v \:.\: w + u \:.\: v' \:.\: w + u \:.\: v \:.\: w'$$

Contoh

$$y = (x^2 + 3x + 4)(6x + 2)$$

\begin{equation*}
\begin{split}
u & = x^2 + 3x + 4 \rightarrow u' = 2x + 3 \\\\
v & = 6x + 2 \rightarrow v' = 6 \\\\
y' & = u' \:.\: v + u \:.\: v' \\\\
y' & = ( 2x + 3) \:.\: (6x + 2) + (x^2 + 3x + 4) \:.\: 6 \\\\
y' & = 12x^2 + 18x + 4x + 6 + 6x^2 + 18x + 24 \\\\
y' & = 18x^2 + 40x + 30
\end{split}
\end{equation*}

###### Turunan Bentuk Pembagian

$$y = \dfrac uv \rightarrow y' = \dfrac {u' \:.\: v - u \:.\: v'}{v^2}$$

Contoh

$$y = \dfrac{2x}{3x + 1}$$

\begin{equation*}
\begin{split}
u & = 2x \rightarrow u' = 2 \\\\
v & = 3x + 1 \rightarrow v' = 3 \\\\
y' & = \frac {u' \:.\: v - u \:.\: v'}{v^2} \\\\
y' & = \frac {2 \:.\: (3x + 1) - 2x \:.\: 3}{(3x + 1)^2} \\\\
y' & = \frac {6x + 2 - 6x}{(3x + 1)^2} \\\\
y' & = \frac {2}{(3x + 1)^2}
\end{split}
\end{equation*}