# Derivative of cotx formula

## Formula

$\dfrac{d}{dx}{\, (\cot{x})} \,=\, -\csc^2{x} \,\,$ (or) $\,\, -\operatorname{cosec}^2{x}$

The derivative of cot function with respect to a variable is equal to negative of square of the cosecant function. It is read as the differentiation of $\cot{x}$ function with respect to $x$ is equal to $–\csc^2x$.

### Introduction

The cotangent function is written as $\cot{x}$ in mathematics if $x$ is used to represent a variable. In differential calculus, the differentiation of the cot function with respect to $x$ is written in the following mathematical form.

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

The derivative of $\cot{x}$ function with respect to $x$ is also written as $\dfrac{d{\,(\cot{x})}}{dx}$. It is also written as ${(\cot{x})}’$ simply in differential calculus.

#### Other form

The formula for derivative of the cot function can be written in the form of any variable.

$(1) \,\,\,$ $\dfrac{d}{db}{\, (\cot{b})} \,=\, -\csc^2{b}$

$(2) \,\,\,$ $\dfrac{d}{dp}{\, (\cot{p})} \,=\, -\csc^2{p}$

$(3) \,\,\,$ $\dfrac{d}{dy}{\, (\cot{y})} \,=\, -\csc^2{y}$

### Proof

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

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