Implicit differentiation for ⬅️BOTH SIDES➡️ of the equation 🤔 #apcalculus #apcalc #unit3 #shorts

In today's video, we're diving into the intricacies of differentiation, focusing on how to handle functions involving both x and y, and emphasizing the importance of applying derivative rules correctly, including the product rule, when variables other than x are present. This is a fundamental skill in AP Calculus, especially when dealing with implicit differentiation.

When differentiating a function with respect to x, and the function includes y, which is itself a function of x, it's crucial to remember that the derivative of y with respect to x is dy/dx or y'. This notation reminds us to apply the chain rule whenever we differentiate an expression involving y.

This approach underscores the seamless integration of derivative rules across functions involving both x and y. It reinforces the necessity of differentiating both sides of an equation, applying familiar rules like the product rule, and recognizing when to multiply by dy/dx} to account for the derivative of y with respect to x.

#APCalculus #Differentiation #ImplicitDifferentiation #ProductRule #CalculusTutorial #MathConcepts

Unit 3 of AP Calculus is all about Differentiation: Composite, Implicit, and Inverse Functions:
3.1 The Chain Rule
3.2 Implicit Differentiation
3.3 Differentiating Inverse Functions
3.4 Differentiating Inverse Trigonometric Functions
3.5 Selecting Procedures for Calculating Derivatives
3.6 Calculating Higher-Order Derivatives

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Видео Implicit differentiation for ⬅️BOTH SIDES➡️ of the equation 🤔 #apcalculus #apcalc #unit3 #shorts канала Krista King