Derivative Rules Derivatives = rates of change = marginal = tangent line slopes Constant Rule: Power Rule: Coefficient Rule: Sum/Difference Rule:

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Presentation transcript:

Derivative Rules Derivatives = rates of change = marginal = tangent line slopes Constant Rule: Power Rule: Coefficient Rule: Sum/Difference Rule:

Example 1 Example 2

Example 3 x y 1 Find the tangent line at x = 2.

Example 4 Given the demand function based on price: Find the rate of change of demand with respect to price and explain the value when If price demand is expected to

Example 5 Given the cost function based on level of production: Find the rate of change of average cost and what level of production has a rate of change value of 0. Average cost is changing

Example 6 Given the cost function based on level of water impurity, p percent: Find the rate of change of cost when impurities account for 10% It would cost about