Main /

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

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,

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

*Sources:*

*Recommended:*

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 CalculusSingleVariablesDerivativeOfSine

Lars

Contact by Snail!

Lars Eighner

APT 1191

8800 N IH 35

AUSTIN TX 78753

USA

Help

**The best way to look for anything in LarsWiki is to use the search bar.**

Physics Pages

- Classical Mechanics Bibliography
- Classical Mechanics Study Sources
- Physics About Physics
- Physics Classical Mechanics
- Physics Index
- Physics Quantum Notions
- Physics Template
- Quantum Physics
- Quantum Physics Bibliography
- Quantum Physics Study Sources
- Quantum Physics Syllabus
- Quarks
- Table of Physical Formulas & Constants
- The Blackbody Problem
- Units and Dimentional Analysis
- Vector Math for Quantum Mechanics

Math Pages

- Derivative of 1/x from Definition.
- (cos θ - 1) / θ = 1
- Algebra Example of Factoring
- Algebra Refresher Exercises
- Binomial Coefficients
- Binomial Theorem
- Coordinates Example
- Derivative of a Function at a Point
- Differential Sum Rule Demonstrated
- Differentiation
- Geometric Interpretation of Derivative
- Geometry
- Geometry of Trig Functions
- Graphing in Two Dimensions
- Hyperbolic Functions
- Implicit Differentiation
- Lim θ → 0 sin(θ) / θ = 1
- Linear Algebra
- Math About Math
- Math Analytic Geometry
- Math Formulas
- Math Function & Expression Index
- Math Index
- Math Markup
- Math Work Template
- Matrix Introduction
- Overview of The Calculus
- Remedial Trigonometry
- Table of Derivatives
- Table of Derivatives, Integrals, & Constants
- Table of Integrals
- Techniques of Integration
- The Calculus of Single Variables
- The Derivative of Arc Cotangent
- The Derivative of Arc Coversed Cosine
- The Derivative of Arc Coversed Sine
- The Derivative of Arc Versed Cosine
- The Derivative of Arc Versed Sine
- The Derivative of Arccosine
- The Derivative of Cosecant
- The Derivative of Cosine
- The Derivative of Cotangent
- The Derivative of Coversed Cosine
- The Derivative of Coversed Sine
- The Derivative of Haversed Sine
- The Derivative of Secant
- The Derivative of Sine
- The Derivative of Versed Cosine
- The Derivative of Versed Sine
- The Fundamental Theorem of Calculus
- The Witch of Agnesi
- Trigonometric Substitution Suggestions
- Vectors

Math Exercises

- Algebra Refresher Exercises Worked
- Calculus Polynomial Graph Exercises
- Calculus Polynomial Graph Exercises Answers
- Calculus Polynomial Graph Exercises Worked
- Calculus Rule Exercises
- Calculus Rule Exercises Answers
- Calculus Rule Exercises Worked
- Composite Exercises Answers
- Composite Function Exercises Worked
- Composition Function Exercises
- Implicit Differentiation Exercises
- Implicit Differentiation Exercises Answers
- Implicit Differentiation Exercises Worked
- Integration by Substitution Exercises
- Integration by Substitution Exercises Answers
- Integration by Substitution Exercises Worked
- Integration Exercises
- Integration Exercises Answers
- Integration Exercises Worked
- Limit Exercises
- Limit Exercises Answers
- Limit Exercises Worked
- Log and Exponential Differentiation Exercises
- Log and Exponential Differentiation Exercises Answers
- Log and Exponential Differentiation Exercises Worked

Math Tools

Sections