Differentiating x 🤔vs.🤔 differentiating y #apcalculus #apcalc #unit3 #shorts

In Unit 3 our focus shifts towards implicit differentiation, particularly the differentiation of y, which is a critical technique for dealing with equations where y is defined implicitly as a function of x. This means that when we take the derivative of y, we initially approach it as we would approach x. However, there's an essential additional step: we must multiply the derivative by y’ (dy/dx) to account for the fact that y is a function of x. This is essentially applying the chain rule to the derivative of y.

For example, when we differentiate 3x^2 using the power rule, we straightforwardly arrive at 6x. But when we encounter 3y^2, the differentiation process begins similarly, treating y as we would x, leading us to a derivative of 6y. The crucial next step involves multiplying this result by y’ (or dy/dx), making the actual derivative 6yy’. This step is vital for correctly applying implicit differentiation and understanding the relationship between y and x.

#APCalculus #ImplicitDifferentiation #DerivativeRules #MathTutorial #CalculusConcepts

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

_____

For extra help with your AP Calc (AB or BC), get my Ultimate Review Packet to help you review all year long and get prepared for the AP test: