Calc 2.5b
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This document discusses techniques for implicitly differentiating second derivatives and provides examples of implicit differentiation. It notes that the second derivative can often be simplified by making substitutions and avoiding full simplification. It also discusses identifying when to use the product rule and chain rule during implicit differentiation and distinguishing constants as coefficients versus terms. Examples provided include finding the normal line equation to a circle at a given point.
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![That was intense! Often we are not interested in the simplest form of the derivative, but in calculating a number from that form, so we can substitute in x and y after taking derivative, even without other simplification, and be okay. Find equations for the normal line to the circle at the given point. at point (3, 4). [A normal line is perpendicular to the tangent line at the point.] In modified point slope form, Simplify and you get or](https://image.slidesharecdn.com/calc2-5b-110926233000-phpapp02/85/Calc-2-5b-3-320.jpg)
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Calc 2.5b
- 1. 2.5b Implicit Differentiation Second-derivatives and more
- 2. Simplifying 2 nd Derivatives with Substitutions Find in terms of x and y for Make a substitution Look for one last substitution Look familiar?
- 3. That was intense! Often we are not interested in the simplest form of the derivative, but in calculating a number from that form, so we can substitute in x and y after taking derivative, even without other simplification, and be okay. Find equations for the normal line to the circle at the given point. at point (3, 4). [A normal line is perpendicular to the tangent line at the point.] In modified point slope form, Simplify and you get or
- 4. Implicit Differentiation things to watch out for: Identifying when to use product rule! Identifying when to use chain rule ! Identifying constants as coefficients or as terms! Product rule, coefficient Chain rule Constant
- 5. Assignment 2.5b p. 146 #27-41 odd, 45-49 odd