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.