Math Doubts

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.

Math Doubts
Math Doubts is a best place to learn mathematics and from basics to advanced scientific level for students, teachers and researchers. Know more
Follow us on Social Media
Math Problems

Learn how to solve easy to difficult mathematics problems of all topics in various methods with step by step process and also maths questions for practising.

Learn more