4-C. Basic Differentiation Rules
Instructions:
- Use the input box for f(x) to define a function. Use the slider tools for k and b to adjust the graph of g(x) = k f(x) + b. Observe how the numbers k and b affect the graph of g(x).
- Use the "tangents" checkbox to show / hide tangent line segments on the graphs of f and g.
- Click the "Trace Derivatives" button to sketch a graph of the derivative functions f'(x) and g'(x). Use the checkboxes for f'(x) and g'(x) to show / hide their graphs.
Basic Differentiation Rules
There are basically two types of shortcuts for finding derivatives: derivative formulas and differentiation rules.
A derivative formula uses the formula for a simple function (i.e., no extra operations) to tell you the formula of the derivative function. These are rules like or .
A differentiation rule tells us how the differentiation operator interacts with function operations like addition, subtraction, and constant multiples. (Later we will also learn rules for composition, multiplication, and division.) For example,
Notice that we don't need to know what f and g are to use this rule; it applies to the operation "+", not the particular functions being added together.