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Business Calculus Derivative Definition. 1.4 The Derivative The mathematical name of the formula is the derivative of f with respect to x. This is the.

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Presentation on theme: "Business Calculus Derivative Definition. 1.4 The Derivative The mathematical name of the formula is the derivative of f with respect to x. This is the."— Presentation transcript:

1 Business Calculus Derivative Definition

2 1.4 The Derivative The mathematical name of the formula is the derivative of f with respect to x. This is the same formula used for instantaneous rate of change, except that we are not given a specific value for x.

3  Equivalent statements: 1. The derivative of f (x) at x = c, or. 2. The (instantaneous) rate of change of y with respect to x at x = c. 3. The slope of the tangent line to f (x) at x = c. 4. The slope of the curve y = f (x) at x = c.  The units of the derivative are. output units input units  Notation for derivative of y = f (x): 1. 2. 3. 4.

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