#Derivatives of Sine and Cosine Functions

#Table of Contents

1. Introduction
2. Differentiating Sin x and Cos x
3. Differentiating Sin kx and Cos kx
4. Worked Examples
5. Using the Definition of a Derivative
6. Glossary
7. Practice Questions
8. Summary and Key Takeaways

#Introduction

In calculus, understanding how to differentiate sine and cosine functions is fundamental. This guide covers the rules for differentiating these trigonometric functions, including their more complex forms, and provides worked examples and practice questions to help solidify your understanding.

#Differentiating Sin x and Cos x

#Key Concepts

• If $f(x) = \sin x$,

• If $g(x) = \cos x$,

• If $h(x) = -\sin x$,

• If $j(x) = -\cos x$,

• This sequence then repeats.

#Differentiating Sin kx and Cos kx

When dealing with functions of the form $\sin(kx)$ and $\cos(kx)$, the differentiation involves the chain rule.

#Ke...