RUMUS DASAR
| F(x) | F'(x) |
| \(\sin x\) | \(\cos x\) |
| \(\cos x\) | \(- \sin x\) |
| \(\tan x\) | \(\sec^2 x\) |
| \(\cot x\) | \(- \csc^2 x\) |
| \(\sec x\) | \(\sec x \tan x\) |
| \(\csc x\) | \(- \csc x \cot x\) |
ATURAN BERANTAI
\(\dfrac {dy}{dx} = \dfrac {dy}{du} \:.\: \dfrac {du}{dx}\)
Contoh 01
Tentukan turunan pertama dari \(y = \sin \: (2x + 5)\).
\begin{equation*} \begin{split} & u =2x + 5 \\\\ & \frac {du}{dx} = 2 \\\\ \end{split} \end{equation*}
\begin{equation*} \begin{split} & y = \sin u \\\\ & \frac {dy}{dx} = \frac {dy}{du} \:.\: \frac {du}{dx} \\\\ & \frac {dy}{dx} = \cos u \:.\: 2 \\\\ & \frac {dy}{dx} = 2 \:.\: \cos \: (2x + 5) \end{split} \end{equation*}
Contoh 02
Tentukan turunan pertama dari \(y = \sin^3 x\).
\begin{equation*} \begin{split} & u =\sin x \\\\ & \frac {du}{dx} = \cos x \\\\ \end{split} \end{equation*}
\begin{equation*} \begin{split} & y = u^3 \\\\ & \frac {dy}{dx} = \frac {dy}{du} \:.\: \frac {du}{dx} \\\\ & \frac {dy}{dx} = 3u^2 \:.\: \cos x \\\\ & \frac {dy}{dx} = 3 \cos x \sin^2 x \end{split} \end{equation*}