Math Doubts

Derivative of cosx


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

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 $\sin{x}$.


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.

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

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


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

Math Doubts

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 math problems in different methods with understandable steps and worksheets on every concept for your practice.

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.

Copyright © 2012 - 2022 Math Doubts, All Rights Reserved