Difference between revisions of "Math 22 Implicit Differentiation"
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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> |
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| + | Therefore, we can use the procedure called '''implicit differentiation''' | ||
Revision as of 09:12, 25 July 2020
Implicit Differentiation
Consider the equation . To find , we can rewrite the equation as , then differentiate as usual. ie: , so . This is called explicit differentiation. However, sometimes, it is difficult to express as a function of explicitly. For example:
Therefore, we can use the procedure called implicit differentiation
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