Section 2.6 Implicit Differentiation
Discover the concept of implicit differentiation through examples such as the folium of Descartes, defined by the equation (x^3 + y^3 = 6xy). This curve cannot be explicitly expressed as (y = f(x)), meaning that (y) is implicitly dependent on (x). Learn how to differentiate the equation (F(x, y) = 0) with respect to (x) without needing to solve for (y) in terms of (x). This method is essential for handling relationships where one variable cannot easily be isolated.
Section 2.6 Implicit Differentiation
E N D
Presentation Transcript
Section 2.6 Implicit Differentiation Math 1231: Single-Variable Calculus
Implicit Function • The folium of Descartes, defined by x3+y3 = 6xy, cannot be EXPLICITLY • written in the form of y = f(x). • We say that y IMPLICITLY depends on x; • or in other words, y = f(x) is a function IMPLICITLY defined through • x3 + [f(x)]3 = 6xf(x).
Implicit Differentiation Given F(x,y) = 0, how to differentiate y with respect to x? • Implicit Differentiation!!! • No need to solve F(x,y)=0 for y in term of x in order to take the derivative of y.
