Implicit Differentiation

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What is Implicit Differentiation?

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Implicit differentiation is a technique used to differentiate equations where the dependent and independent variables are not separated. It allows us to find the derivative of y with respect to x when y is defined implicitly as a function of x.

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What is the derivative of a function?

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The derivative of a function at a point is the slope of the tangent line to the graph of the function at that point. It represents the rate of change of the function with respect to its variable.

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What is the formula for the derivative of y with respect to x in implicit differentiation?

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What is the slope of the tangent line?

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The slope of the tangent line at a point on a curve is given by the derivative of the function at that point.

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What does the term 'secant line' refer to?

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A secant line is a line that intersects a curve at two or more points. The slope of the secant line between two points on the curve approximates the average rate of change of the function between those points.

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What is the relationship between the derivative and the slope of a curve?

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The derivative at a point gives the slope of the tangent line to the curve at that point, indicating how steep the curve is at that location.