Math 22 Implicit Differentiation - Revision history

Tphan046: /* Guidelines for Implicit Differentiation */

2020-07-27T14:28:27Z

Guidelines for Implicit Differentiation

2020-07-25T17:17:05Z

2020-07-25T17:16:58Z

Guidelines for Implicit Differentiation

2020-07-25T17:16:29Z

Guidelines for Implicit Differentiation

2020-07-25T17:16:15Z

Guidelines for Implicit Differentiation

2020-07-25T17:16:00Z

Implicit Differentiation

2020-07-25T17:12:19Z

Implicit Differentiation

2020-07-25T17:12:07Z

Implicit Differentiation

2020-07-25T17:04:26Z

2020-07-25T16:51:57Z

Implicit Differentiation

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-Under Construction
+'''Example''': Find <math>\frac{dy}{dx}</math> of
 [[Math_22| '''Return to Topics Page''']]
 '''This page were made by [[Contributors|Tri Phan]]'''

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 Under Construction
 [[Math_22| '''Return to Topics Page''']]
 '''This page were made by [[Contributors|Tri Phan]]'''

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-Solve for  by dividing both sides of the equation by the left-hand factor that does not contain .
+Under Construction
 [[Math_22| '''Return to Topics Page''']]
 '''This page were made by [[Contributors|Tri Phan]]'''

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 . Differentiate both sides of the equation with respect to <math>x</math>.
 . Collect all terms involving <math>\frac{dy}{dx}</math> on the left side of the equation and move all other terms to the right side of the equation
 . Factor <math>\frac{dy}{dx}</math> out of the left side of the equation.
 . Solve for <math>\frac{dy}{dx}</math> by dividing both sides of the equation by the left-hand factor that does not contain <math>\frac{dy}{dx}</math>.
 [[Math_22| '''Return to Topics Page''']]
 '''This page were made by [[Contributors|Tri Phan]]'''

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 ==Guidelines for Implicit Differentiation==
    Consider an equation involving <math>x</math> and <math>y</math> in which <math>y</math> is a differentiable function of <math>x</math>. You can use the steps below to find <math>\frac{dy}{dx}</math>.
-. Differentiate both sides of the equation with respect to <math>x</math.
+. Differentiate both sides of the equation with respect to <math>x</math>.
 . Collect all terms involving <math>\frac{dy}{dx}</math> on the left side of the equation and move all other terms to the right side of the equation
    Under Construction

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 ==Implicit Differentiation==
-Consider the equation <math>x^2y=5</math>. To find <math>\frac{dy}{dx}</math>, we can rewrite the equation as <math>y=\frac{5}{x^2}</math>, then differentiate as usual. ie: <math>y=\frac{5}{x^2}=5x^{-2}</math>, so <math>\frac{dy}{dx}=-10x^{-3}</math>. This is called explicit differentiation. However, sometimes, it is difficult to express <math>y</math> as a function of <math>x</math> explicitly. For example: <math>y^2-2x+4xy=5</math>
+Consider the equation <math>x^2y=5</math>. To find <math>\frac{dy}{dx}</math>, we can rewrite the equation as <math>y=\frac{5}{x^2}</math>, then differentiate as usual. ie: <math>y=\frac{5}{x^2}=5x^{-2}</math>, so <math>\frac{dy}{dx}=-10x^{-3}</math>. This is called explicit differentiation.
 Therefore, we can use the procedure called '''implicit differentiation'''

← Older revision		Revision as of 17:12, 25 July 2020
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	==Implicit Differentiation==		==Implicit Differentiation==

−	Consider the equation <math>x^2y=5</math>. To find <math>\frac{dy}{dx}</math>, we can rewrite the equation as <math>y=\frac{5}{x^2}</math>, then differentiate as usual. ie: <math>y=\frac{5}{x^2}=5x^{-2}</math>, so <math>\frac{dy}{dx}=-10x^{-3}</math>	+	Consider the equation <math>x^2y=5</math>. To find <math>\frac{dy}{dx}</math>, we can rewrite the equation as <math>y=\frac{5}{x^2}</math>, then differentiate as usual. ie: <math>y=\frac{5}{x^2}=5x^{-2}</math>, so <math>\frac{dy}{dx}=-10x^{-3}</math>. This is called explicit differentiation. However, sometimes, it is difficult to express <math>y</math> as a function of <math>x</math> explicitly. For example: <math>y^2-2x+4xy=5</math>
		+
		+	Therefore, we can use the procedure called '''implicit differentiation'''

← Older revision		Revision as of 17:04, 25 July 2020
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	==Implicit Differentiation==		==Implicit Differentiation==
		+
		+	Consider the equation <math>x^2y=5</math>. To find <math>\frac{dy}{dx}</math>, we can rewrite the equation as <math>y=\frac{5}{x^2}</math>, then differentiate as usual. ie: <math>y=\frac{5}{x^2}=5x^{-2}</math>, so <math>\frac{dy}{dx}=-10x^{-3}</math>
		+

	Under Construction		Under Construction