Defining the Derivative - Revision history

Lila: /* Licensing */

2021-10-27T20:53:37Z

Licensing

Lila: /* Resources */

2021-10-27T20:51:56Z

Resources

Lila: /* The Definition of the Derivative */

2021-10-18T18:57:36Z

The Definition of the Derivative

Lila at 22:19, 28 September 2021

2021-09-28T22:19:13Z

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James.kercheville: Added video links

2020-08-24T02:34:54Z

Added video links

James.kercheville: Added links for PowerPoint and worksheet

2020-08-12T20:14:09Z

Added links for PowerPoint and worksheet

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* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Defining%20the%20Derivative/MAT1214-3.1DefiningTheDerivativePwPt.pptx Defining the Derivative] PowerPoint file created by Dr. Sara Shirinkam, UTSA.

* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Defining%20the%20Derivative/MAT1214-DefiningTheDerivative_RateOfChangeWS.pdf Defining the Derivative Worksheet 1]

← Older revision		Revision as of 20:53, 27 October 2021
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	Content obtained and/or adapted from:		Content obtained and/or adapted from:
	* [https://en.wikibooks.org/wiki/A-level_Mathematics/OCR/C1/Differentiation Differentiation, Wikibooks: A-level Mathematics/OCR/C1] under a CC BY-SA license		* [https://en.wikibooks.org/wiki/A-level_Mathematics/OCR/C1/Differentiation Differentiation, Wikibooks: A-level Mathematics/OCR/C1] under a CC BY-SA license
		+	* [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 20:51, 27 October 2021
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	* [https://youtu.be/5yfh5cf4-0w Calculus 1 - Derivatives] by The Organic Chemistry Tutor		* [https://youtu.be/5yfh5cf4-0w Calculus 1 - Derivatives] by The Organic Chemistry Tutor
		+
		+	==Licensing==
		+	Content obtained and/or adapted from:
		+	* [https://en.wikibooks.org/wiki/A-level_Mathematics/OCR/C1/Differentiation Differentiation, Wikibooks: A-level Mathematics/OCR/C1] under a CC BY-SA license

← Older revision		Revision as of 18:57, 18 October 2021
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	* <math>D(f(x))=2x</math>		* <math>D(f(x))=2x</math>

		+	===Tangent Lines===
		+	Since we can find the gradient of a function at any point we can also find the equation of the tangent line to the function at any point:
		+
		+	What is the equation of the tangent line for the curve <math>y = x^2 + 3x -16</math> at the point x = -4?
		+
		+	First we need to find the derivative of the equation.
		+
		+	<math>\frac{dy}{dx} = 2x + 3</math>
		+
		+	Then we find the gradient at the point x = -4.
		+
		+	<math>2\left ( -4 \right) + 3 = -5</math>
		+
		+	Using the original function we find the corresponding y value to the x value at the point of tangency.
		+
		+	<math>y = -4^2 + 3 \left (-4 \right) -16 = -12</math>
		+
		+	Then we use the point-gradient equation to find the equation.
		+
		+	<math>y + 12 = -5 \left ( x + 4 \right )</math> so the equation of the tangent line is y = -5x - 32....

	==Resources==		==Resources==

← Older revision		Revision as of 02:34, 24 August 2020
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	* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Defining%20the%20Derivative/MAT1214-DefiningTheDerivative_RateOfChangeWS.pdf Defining the Derivative Worksheet 1]		* [https://mathresearch.utsa.edu/wikiFiles/MAT1214/Defining%20the%20Derivative/MAT1214-DefiningTheDerivative_RateOfChangeWS.pdf Defining the Derivative Worksheet 1]
		+
		+
		+	* [https://youtu.be/2wH-g60EJ18 Understanding the Definition of the Derivative] by patrickJMT
		+
		+	* [https://youtu.be/vzDYOHETFlo Finding a Derivative Using the Definition of a Derivative] by patrickJMT
		+
		+	* [https://youtu.be/-aTLjoDT1GQ Definition of the Derivative] by The Organic Chemistry Tutor
		+
		+	* [https://youtu.be/5yfh5cf4-0w Calculus 1 - Derivatives] by The Organic Chemistry Tutor