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Business Calculus Derivatives
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1.5 – 1.7 Derivative Rules Linear Rule: Constant Rule: Power Rule: Coefficient Rule: Sum/Difference Rule:
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If a function does not look like one of the rules, we must rewrite the function so that it does. Applications When asked for the rate at which a quantity is growing or declining between two values, this is an average rate of change. When asked for the rate of change at a single value, use the derivative.
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More derivative rules 1.6 Product Rule: Product Rule: "derivative of the first times the second + the first times the derivative of the second"
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1.6 Quotient Rule: Quotient Rule: “denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the denominator squared”
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1.7 The Chain Rule : "The derivative of the outside times the derivative of the inside."
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1.8 Higher Order Derivatives The second derivative is found by taking the derivative of the first derivative. Notation for the second derivative of y = f (x): 1. 2. 3. 4. Notation for the third derivative of y = f (x): 1. 2. 3. 4.
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