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Implicit Derivatives

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Given the equation

How do we find ?

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Let's check to see if implicit differentiation is reasonable.

Differentiate in two ways.

Implicit

Explicit

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EX 1 Find for the following equations.

a)

b) 9x2+4y2 = 36 

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To convince ourselves that is works, let's look at a familiar equation.

Find the equation of the tangent line at the point (-4,3) on this circle.

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EX 2 Find the equation of the tangent line at the indicated point.

 

at (1,0)

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Power Rule (revisited): Basically the power rule can now be used with rational exponents.

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EX 3 Find y' if

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