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Business Calculus

Business Calculus. Derivatives. 1.5 – 1.7 Derivative Rules. Linear Rule: . Constant Rule: . Power Rule: . Coefficient Rule: . Sum/Difference Rule:

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Business Calculus

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  1. Business Calculus Derivatives

  2. 1.5 – 1.7 Derivative Rules • Linear Rule:  • Constant Rule:  • Power Rule:  • Coefficient Rule:  • Sum/Difference Rule: 

  3. 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.

  4. More derivative rules 1.6 Product Rule:  Product Rule: "derivative of the first times the second + the first times the derivative of the second"

  5. 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”

  6. 1.7 The Chain Rule :  "The derivative of the outside times the derivative of the inside."

  7. 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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