# Turunan Fungsi Trigonometri

### Turunan Fungsi Trigonometri

##### 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 $$y = \sin \: (2x + 5)$$

Cara pemisalan

\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 u \\\\ & \frac {dy}{dx} = \bbox[5px, border: 2px solid magenta] {2 \:.\: \cos \: (2x + 5)} \end{split} \end{equation*}

Cara langsung

\begin{equation*} \begin{split} & y = \sin \: ({\color {red} 2x + 5}) \\\\ & {\color {blue} \text{turunan dari } 2x + 5 \text{ adalah } 2} \\\\ & {\color {blue} \text{turunan dari } \sin \: (2x + 5) \text{ adalah } \cos \: (2x + 5)} \\\\ & \frac {dy}{dx} = \bbox[5px, border: 2px solid magenta] {2 \:.\: \cos \: (2x + 5)} \end{split} \end{equation*}

Contoh 02

Tentukan turunan pertama dari $$y = \cos^3 x$$

Cara pemisalan

\begin{equation*} \begin{split} & u =\cos x \\\\ & \frac {du}{dx} = - \sin x \end{split} \end{equation*}

\begin{equation*} \begin{split} & y = u^3 \\\\ & \frac {dy}{dx} = \frac {dy}{du} \:.\: \frac {du}{dx} \\\\ & \frac {dy}{dx} = 3 \:.\: u^2 \:.\: -\sin x \\\\ & \frac {dy}{dx} = -3 \:.\: \sin x \:.\: u^2  \\\\ & \frac {dy}{dx} = \bbox[5px, border: 2px solid magenta] {-3 \:.\: \sin x \:.\: \cos^2 x} \end{split} \end{equation*}

Cara langsung

\begin{equation*} \begin{split} & y = \cos^3 x \\\\ & {\color {blue} \text{turunan dari } \cos x \text{ adalah } - \sin x} \\\\ & \frac {dy}{dx} = - \sin x \:.\: 3 \:.\: \cos^2 x \\\\ & \frac {dy}{dx} = \bbox[5px, border: 2px solid magenta] {-3 \:.\: \sin x \:.\: \cos^2 x} \end{split} \end{equation*}