# 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.

Latest Math Topics
Apr 18, 2022
Apr 14, 2022
Mar 18, 2022
Latest Math Problems
Apr 06, 2022

A best free mathematics education website for students, teachers and researchers.

###### Maths Topics

Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.

###### Maths Problems

Learn how to solve the maths problems in different methods with understandable steps.

Learn solutions

###### Subscribe us

You can get the latest updates from us by following to our official page of Math Doubts in one of your favourite social media sites.