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Section 2.6 Implicit Differentiation

Section 2.6 Implicit Differentiation. Math 1231: Single-Variable Calculus. Implicit Function. The folium of Descartes, defined by x 3 + y 3 = 6 xy , cannot be EXPLICITLY written in the form of y = f ( x ). We say that y IMPLICITLY depends on x ;

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Section 2.6 Implicit Differentiation

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  1. Section 2.6 Implicit Differentiation Math 1231: Single-Variable Calculus

  2. 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).

  3. 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.

  4. Examples

  5. More Examples

  6. More Examples

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