06Implicit Differentiation - y . Ex . Find y if 4 4 16 x y...

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I MPLICIT D IFFERENTIATION Some functions are expressed explicitly in terms of another variable (y = ), but others are defined implicitly by a relation between x and y such as . 25 2 2 = + y x We could solve for y and then take the derivative, or we could use a process called implicit differentiation . Differentiate both sides of the equation with respect to x , then solve the resulting equation for y . Ex . . 25 2 2 = + y x 2 25 x y - ± = Ex . If 3 3 5 x y + = , use implicit differentiation to find
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Unformatted text preview: y . Ex . Find y if 4 4 16 x y + = . Ex . a) Find dx dy if 36 2 5 4 5 = + + y y x x b) Find the slope of the tangent to the curve 36 2 5 4 5 = + + y y x x at the point (1, 2). Ex . Find the slope of the tangent line to 1 3 2 2 2 3 = + + +-x y x xy y at the point (1, 2). Assign: p.217 # 9, 11-16, 21, 23; Worksheets implicit differentiation...
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06Implicit Differentiation - y . Ex . Find y if 4 4 16 x y...

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