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#### Trigonometric rules for differentiation

The derivatives of the fundamental trigonometric functions are shown here.

Function | Derivative |
---|---|

\(\sin(x)\) | \(\cos(x)\) |

\(\cos(x)\) | \(-\sin(x)\) |

\(\tan(x)\) | \(\frac{1}{\cos(x)^2}\) |

#### Let’s practice!

Determine the derivative of the function

\({-5}\cdot\mathrm{sin}\left(x\right)-4\)

We first apply the sum rule:

\(\frac{d}{dx}\left({-5}\cdot\mathrm{sin}\left(x\right)-4\right)=\frac{d}{dx}\left({-5}\cdot\mathrm{sin}\left(x\right)\right)+\frac{d}{dx}\left(-4\right)\)

We now apply the product-with-constant and constant rule:

\(\frac{d}{dx}\left({-5}\cdot\mathrm{sin}\left(x\right)-4\right)={-5}\cdot\frac{d}{dx}\left(\mathrm{sin}\left(x\right)\right)+0\)

The derivative of \(\sin(x)\) is \(\cos(x)\)

\(\frac{d}{dx}\left({-5}\cdot\mathrm{sin}\left(x\right)-4\right)={-5}\cdot\mathrm{cos}\left(x\right)\)