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 Questions

The math problems with solutions to learn how to solve a problem.

Learn solutions

Math Worksheets

The math worksheets with answers for your practice with examples.

Practice now

Math Videos

The math videos tutorials with visual graphics to learn every concept.

Watch now

Subscribe us

Get the latest math updates from the Math Doubts by subscribing us.

Learn more

Math Doubts

A free math education service for students to learn every math concept easily, for teachers to teach mathematics understandably and for mathematicians to share their maths researching projects.

Copyright © 2012 - 2023 Math Doubts, All Rights Reserved