Calculus 1000A/B Lecture Notes - Lecture 2: Implicit Function, Product Rule
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27 Nov 2018
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CALC 1000A/B Full Course Notes
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Find the slope of the tangent to the curve 2x 5 + x 4 y + y 5 = 36 at the point (1, 2). The problem with this kind of question is that x and y, unlike a fool and his money, are not soon parted. To solve this kind of question, we need to use implicit differentiation. To derive implicitly, we apply the chain rule to y. For example, to differentiate y 2 , we would do the following. Example: if x 2 + y 2 = 25 , find dy dx d dx d dx x 2( 2x + 2y d dx y 2 = 2y . Y x 2 + y 2 d dx. Differentiate 2x 5 + x 4 y + y 5 = 36 . Note here that we will have to use the product rule for the x 4 y term. y d dx x 4 y.
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