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2014 Implicit Differentiation. Calculus BC. Implicit Differentiation. Equation for a line: Explicit Form <One variable given explicitly in terms of the other> Implicit Form <Function implied by the equation> Differentiate the Explicit < Explicit : , y is function of x >

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## 2014 Implicit Differentiation

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**2014 Implicit Differentiation**Calculus BC**Implicit Differentiation**Equation for a line: Explicit Form <One variable given explicitly in terms of the other> Implicit Form <Function implied by the equation> Differentiate the Explicit < Explicit: , y is function of x > Differentiation taking place with respect to x. The derivative is explicit also.**Implicit Differentiation**Equation of circle: To work explicitly; must work two equations Implicit Differentiation is a Short Cut - A method to handle equations that are not easily written explicitly. ( Usually non-functions)**Implicit Differentiation**Find the derivative with respect to x < Assuming - y is a differentiable function of x > Chain Rule Pretend y is some function like so becomes (A) (B) (C) Note: Use the Leibniz form. Leads to Parametric and Related Rates.**Implicit Differentiation**(D) Product Rule (E) Chain Rule**Implicit Differentiation**To find implicitly. EX: Diff Both Sides of equation with respect to x Solve for**EX 1:**(a) Find the derivative at the point ( 5, 3 ) , at ( -1,-3 ) (b) Find where the curve has a horizontal tangent. (c) Find where the curve has vertical tangents.**Ex 2:**< Folium of Descartes >**Why Implicit?**Explicit Form: < Folium of Descartes >**Ex 2 Graph:**< Folium of Descartes > Parametric Form: Plot the Folium of Descartes on your graphing calculator and determine the portion of the folium generated when (a) t < -1 ; (b) -1 < t 0 ; (c) t > 0**2nd Derivatives**EX: Our friendly circle. Find the 2nd Derivative. NOTICE:The second derivative is in terms of x , y , AND dy /dx. The final step will be to substitute back the value of dy / dx into the second derivative.**EX: Find the 2nd Derivative.**2nd Derivatives**EX: Find the Third Derivative.**Higher Derivatives**Last update**• 10/19/10 • p. 162 11 – 29 odd

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