3: Rules for Finding Derivatives
- Page ID
- 147937
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It is tedious to compute a limit every time we need to know the derivative of a function. Fortunately, we can develop a small collection of examples and rules that allow us to compute the derivative of almost any function we are likely to encounter. Many functions involve quantities raised to a constant power, such as polynomials and more complicated combinations like \(y=(\sin x)^4\). So we start by examining powers of a single variable; this gives us a building block for more complicated examples.
- 3.1: The Power Rule
- The power rule addresses the derivative of a power function.
- 3.2: Linearity of the Derivative
- The derivative is a linear operation and behaves "nicely'' with respect to changing its argument function via multiplication by a constant and addition .
- 3.3: The Product Rule
- The product rule is used to construct the derivative of a product of two functions.
- 3.4: The Quotient Rule
- The quotient rule use used to compute the derivative of f(x)/g(x) if we already know f′(x) and g′(x). It is often possible to calculate derivatives in more than one way, as we have already seen. Since every quotient can be written as a product, it is always possible to use the product rule to compute the derivative, though it is not always simpler.
- 3.5: The Chain Rule
- When simple functions are made into more complicated functions (e.g., composite functions), the chain rule can be used to identify the relevant derivative.