Influencing the price elasticity of demand Identifying the bottom line, almost: The price elasticity

Chapter 3: Calculus, Optimization, and You

important rules of differentiation. If you need more than a quick refresher, a great place to go is Calculus For Dummies (John Wiley & Sons) and its online cheat sheet at www.dummies.com/cheatsheet/calculus.

Constant function rule

If variable y is equal to some constant a, its derivative with respect to x is 0, or if

For example,

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Power function rule

A power function indicates that the variable x is raised to a constant power k.

The derivative of y with respect to x equals k multiplied by x raised to the k-1 power, or

For example,

The power function rule is extremely powerful! You can use it with a variety of exponents. For example,

can be rewritten as

Be careful with this last derivative. When a variable with an exponent appears in the denominator, such as x3 in the previous equation, the variable can be moved to the numerator, but the exponent becomes negative. So, 4/x3 becomes 4x-3. Then when you take the derivative, make sure you subtract 1 from –3 to get –4.

As another example, consider