Skip to content

# Lars Eighner's Homepage

## LarsWiki

calumus meretrix et gladio innocentis

### The Derivative of Cosine Cosine
##### Contents {$y = \cos(x)$} and {$y=\arccos(x)$}

{$$\begin{gather} {d \over {dx}} \cos x = \lim_{h \rightarrow 0} {{ \cos(x+h) - \cos x} \over h} \cr = \lim_{h \rightarrow 0} {{ \cos(x) \cos(h) - \sin (x) \sin (h) - \cos(x)} \over h} \cr = \lim_{h \rightarrow 0} {{ \cos(x)( \cos(h) - 1) - \sin (x) \sin (h)} \over h} \cr = \lim_{h \rightarrow 0} \left[ \cos(x) \left( {{\cos(h) - 1} \over h} \right) - \sin (x) \left( {{\sin (h)} \over h} \right) \right] \end{gather}$$}

The limit of {$(\cos(h)-1)/h$} is known to be 0 from a previous result, and likewise {$\sin(x)/h$} is known to be 1. Therefore,

{$${d \over {dx}} \cos x = - \sin x$$}

Sources:

Recommended:

Category: Math Calculus

No comments yet.

This is a student's notebook. I am not responsible if you copy it for homework, and it turns out to be wrong.

Figures are often enhanced by hand editing; the same results may not be achieved with source sites and source apps.

Backlinks

This page is CalculusSingleVariablesDerivativeOfCosine

### December 23, 2018

• HomePage
• WikiSandbox

Lars

Contact by Snail!

Lars Eighner
APT 1191
8800 N IH 35
AUSTIN TX 78753
USA

Help