Implicit differentiation Review

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What is implicit differentiation?

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Implicit differentiation is a technique used to find the derivative of a function defined implicitly by an equation involving both x and y, rather than explicitly solving for y.

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What is the chain rule in the context of implicit differentiation?

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The chain rule states that if y is a function of x, then the derivative of a composite function is the derivative of the outer function times the derivative of the inner function.

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What is the product rule in differentiation?

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What is the significance of the implicit function theorem?

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The implicit function theorem provides conditions under which a relation defines a function implicitly, allowing for the differentiation of y with respect to x.

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How do you find the slope of a tangent line using implicit differentiation?

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What is the relationship between implicit differentiation and related rates?

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Implicit differentiation is often used in related rates problems to find the rate of change of one variable with respect to another when both are related by an equation.