# Derivative of cosx

## Formula

$\dfrac{d}{dx}{\, (\cos{x})} \,=\, -\sin{x}$

The differentiation or derivative of cos function with respect to a variable is equal to negative sine. This formula is read as the derivative of $\cos{x}$ with respect to $x$ is equal to negative $\sin{x}$.

### Introduction

If $x$ is used to represent a variable, then the cosine function is written as $\cos{x}$ in mathematics. The derivative of the cos function with respect to $x$ is written in mathematical form as follows.

$\dfrac{d}{dx}{\, (\cos{x})}$

Mathematically, the differentiation of the $\cos{x}$ function with respect to $x$ is also written as $\dfrac{d{\,(\cos{x})}}{dx}$ and also written as ${(\cos{x})}’$ in simple form.

#### Other form

The derivative of the cos function can be written in terms of any variable.

$(1) \,\,\,$ $\dfrac{d}{dr}{\, (\cos{r})} \,=\, -\sin{r}$

$(2) \,\,\,$ $\dfrac{d}{dz}{\, (\cos{z})} \,=\, -\sin{z}$

### Proof

Learn how to derive the derivative of the cosine function from first principle in differential calculus.

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