AP Calculus - Unit 2 - Section 9 - Implicit Differentiation скачать в хорошем качестве

AP Calculus - Unit 2 - Section 9 - Implicit Differentiation

Struggling with derivatives where 'y' and 'x' are all tangled up? This video is for calculus students, especially those preparing for AP Calculus, who want to master implicit differentiation. This tutorial dives deep into implicit differentiation, explaining how to find derivatives when equations aren't explicitly solved for 'y'. You'll learn the essential role of the chain rule in these scenarios, how to apply product and quotient rules within implicit differentiation, and even how to calculate second derivatives. Understanding this technique is crucial for analyzing the slopes of tangent lines for complex curves. Chapters: Introduction to Implicit Differentiation 00:00 What is Implicit Differentiation? 00:00 Chain Rule and Implicit Differentiation 01:49 Example 1: Basic Implicit Differentiation 03:33 Example 2: Product Rule with Implicit Differentiation 04:58 Example 3: Inverse Sine and Implicit Differentiation 07:59 Conceptual Understanding of Implicit Differentiation 09:28 Finding Derivative at a Specific Point 10:05 Calculating the Second Derivative 11:56 Summary and Additional Resources 14:38 Key Takeaways: Implicit differentiation is used when 'y' isn't easily written as a function of 'x'. You take the derivative of both sides of the equation. Every time you take the derivative of a 'y' term, you must multiply by dy/dx (because of the chain rule). After taking derivatives, gather all dy/dx terms on one side and everything else on the other. Factor out dy/dx and solve for it. The derivative will often have both 'x' and 'y' in it, so you need both coordinates to find the slope at a point. Finding the second derivative involves taking the derivative of the first derivative and substituting the dy/dx expression. What you'll practice: Applying the chain rule in implicit differentiation. Using the product rule and quotient rule with implicit functions. Solving for dy/dx in various implicit equations. Calculating the slope of a tangent line at a specific point on an implicitly defined curve. Finding second derivatives of implicit functions. SEO Keywords: Implicit Differentiation, Calculus Chain Rule, Derivatives of Y, AP Calculus Differentiation, How to find dy/dx, Calculus Implicit Functions, Second Derivative Implicit, Calculus for Parents, Slope of Tangent Line Implicit, Product Rule Implicit Differentiation, Quotient Rule Implicit Differentiation, Calculus help, Multivariable Calculus, Derivatives explained, Advanced Calculus #ImplicitDifferentiation #Calculus #APCalculus #Derivatives #ChainRule If you want to learn more resources we offer, you can check it out at: https://www.bothellstemcoach.com/ap-p... https://www.bothellstemcoach.com/ap-c... https://www.bothellstemcoach.com/ap-p... https://www.bothellstemcoach.com/ap-p...