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,
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
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