The Derivative as a Function - Revision history

Khanh: /* Of a graph of a function */

2022-01-15T22:18:59Z

Of a graph of a function

Lila: /* Resources */

2021-10-27T20:55:33Z

Resources

Khanh at 17:51, 10 October 2021

2021-10-10T17:51:33Z

Show changes

James.kercheville: Added video link

2020-08-28T18:10:44Z

Added video link

James.kercheville: Added video links

2020-08-28T18:08:48Z

Added video links

James.kercheville: Added notes for this topic

2020-08-18T21:41:16Z

Added notes for this topic

James.kercheville: Added links for PowerPoint and worksheet

2020-08-12T20:19:27Z

Added links for PowerPoint and worksheet

New page

* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/The%20Derivative%20as%20a%20Function/MAT1214-3.2TheDerivativeAsAFunctionPwPt.pptx The Derivative as a Function] PowerPoint file created by Dr. Sara Shirinkam, UTSA.

* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/The%20Derivative%20as%20a%20Function/MAT1214-3.2TheDerivativeAsAFunctionWS1.pdf The Derivative as a Function Worksheet 1]

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 This expression is called the '''difference quotient'''. Note that <math>h</math> can be positive or negative — it is perfectly valid to take a secant through any two points on the curve — but cannot be <math>0</math> .
-The definition of the tangent line we gave was not rigorous, since we've only defined limits of ''numbers'' — or, more precisely, of functions that output numbers — not of ''lines''. But we ''can'' define the ''slope'' of the tangent line at a point rigorously, by taking the limit of the slopes of the secant lines from the last paragraph. Having done so, we can ''then'' define the tangent line as well. Note that we cannot simply set <math>h</math> to 0 as this would imply division of 0 by 0 which would yield an undefined result. Instead we must find the [[Calculus/Limits|'''limit''']] of the above expression as <math>h</math> '''tends''' to 0:
+The definition of the tangent line we gave was not rigorous, since we've only defined limits of ''numbers'' — or, more precisely, of functions that output numbers — not of ''lines''. But we ''can'' define the ''slope'' of the tangent line at a point rigorously, by taking the limit of the slopes of the secant lines from the last paragraph. Having done so, we can ''then'' define the tangent line as well. Note that we cannot simply set <math>h</math> to 0 as this would imply division of 0 by 0 which would yield an undefined result. Instead we must find the '''limit''' of the above expression as <math>h</math> '''tends''' to 0:
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← Older revision		Revision as of 20:55, 27 October 2021
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	* [https://youtu.be/fml0-ELYLaE Continuity and Differentiability] by The Organic Chemistry Tutor		* [https://youtu.be/fml0-ELYLaE Continuity and Differentiability] by The Organic Chemistry Tutor
		+
		+	==Licensing==
		+	Content obtained and/or adapted from:
		+	* [https://en.wikibooks.org/wiki/Calculus/Differentiation/Differentiation_Defined Differentiation Defined, Wikibooks: Calculus/Differentiation] under a CC BY-SA license

← Older revision		Revision as of 18:10, 28 August 2020
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	* [https://youtu.be/-aTLjoDT1GQ Definition of the Derivative] by The Organic Chemistry Tutor		* [https://youtu.be/-aTLjoDT1GQ Definition of the Derivative] by The Organic Chemistry Tutor
		+
		+	* [https://youtu.be/fml0-ELYLaE Continuity and Differentiability] by The Organic Chemistry Tutor

← Older revision		Revision as of 18:08, 28 August 2020
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	* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/The%20Derivative%20as%20a%20Function/MAT1214-3.2TheDerivativeAsAFunctionWS1.pdf The Derivative as a Function Worksheet 1]		* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/The%20Derivative%20as%20a%20Function/MAT1214-3.2TheDerivativeAsAFunctionWS1.pdf The Derivative as a Function Worksheet 1]
		+
		+
		+	* [https://youtu.be/vzDYOHETFlo Finding a Derivative Using the Definition of a Derivative] by patrickJMT
		+
		+	* [https://youtu.be/3bmw9UQxbRI Derivative of Root Function Using Definition of a Derivative] by patrickJMT
		+
		+	* [https://youtu.be/WERgBgi4hg4 Derivative Using the Definition, Example 2] by patrickJMT
		+
		+	* [https://youtu.be/-aTLjoDT1GQ Definition of the Derivative] by The Organic Chemistry Tutor

← Older revision		Revision as of 21:41, 18 August 2020
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	* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/The%20Derivative%20as%20a%20Function/MAT1214-3.2TheDerivativeAsAFunctionPwPt.pptx The Derivative as a Function] PowerPoint file created by Dr. Sara Shirinkam, UTSA.		* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/The%20Derivative%20as%20a%20Function/MAT1214-3.2TheDerivativeAsAFunctionPwPt.pptx The Derivative as a Function] PowerPoint file created by Dr. Sara Shirinkam, UTSA.
		+
		+	* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/The%20Derivative%20as%20a%20Function/MAT1214-3.2TheDerivAsFunctionNotes.pdf The Derivative as a Function Notes] created by Instructor Sean Beatty, UTSA.

	* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/The%20Derivative%20as%20a%20Function/MAT1214-3.2TheDerivativeAsAFunctionWS1.pdf The Derivative as a Function Worksheet 1]		* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/The%20Derivative%20as%20a%20Function/MAT1214-3.2TheDerivativeAsAFunctionWS1.pdf The Derivative as a Function Worksheet 1]