Bentuk Perkalian dan Pembagian
\(y = u \:.\: v \rightarrow y' = u' \:.\: v + u \:.\: v'\)
\(y = u \:.\: v \:.\: w \rightarrow y' = u' \:.\: v \:.\: w + u \:.\: v' \:.\: w + u \:.\: v \:.\: w'\)
\(y = \dfrac uv \rightarrow y' = \dfrac {u' \:.\: v - u \:.\: v'}{v^2}\)
Contoh 01
\(y = (x^2 + 3x + 4) \:.\: (6x + 2)\)
\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' & = \bbox[5px, border: 2px solid magenta] {18x^2 + 40x + 30} \end{split} \end{equation*}
Contoh 02
\(y = \dfrac{2x}{3x + 1}\)
\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' & = \bbox[5px, border: 2px solid magenta] {\frac {2}{(3x + 1)^2}} \end{split} \end{equation*}
SOAL LATIHAN