# Turunan Fungsi Trigonometri

## Konsep Dasar

#### 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*}