implicit differentiation

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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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How do you apply implicit differentiation to find dy/dx?

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To apply implicit differentiation, differentiate both sides of the equation with respect to x, treating y as a function of x. Use the chain rule for terms involving 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 y with respect to x is the derivative of y with respect to another variable multiplied by the derivative of that variable with respect to x.

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What is the significance of treating y as a function of x in implicit differentiation?

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Treating y as a function of x allows us to differentiate y with respect to x, which is essential for finding the slope of the tangent line to the curve defined by the implicit equation.

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

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First, find dy/dx using implicit differentiation, then substitute the x and y coordinates of the specific point into the derivative to find the slope.

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