How to define the derivative function f'(x).
How to determine the derivative of a power function.
How to determine the derivative of a linear function.
How to compute the derivative of a polynomial function using two properties of the derivative.
How to use the definition of the derivative to find a derivative formula for exponential functions.
How to infer the derivative of the natural log function using a calculator investigation.
How to define the derivative of a function at a point x=a.
How to recognize and use Newton's and Leibniz's notation for the derivative.
How to determine whether a function f(x) is continuous everywhere on its domain.
How to differentiate a product of two functions.
How to find an antiderivative of a function.
How to evaluate the limit of a function using continuity.
How to find the average value of a function over an interval [a,b].
How to evaluate the limit of a function as x goes to infinity (or minus infinity), and how to determine the horizontal asymptote of its graph.
How to show that polynomial functions are continuous functions.
How to differentiate a composite function when the outside function is the natural logarithm.
How to interpret the derivatives of the cost and revenue functions as marginal cost and marginal revenue.
How to differentiate a composite function.
How to differentiate a composite function when the outside function is a power function.
How to determine one-sided and two-sided limits from the graph of a function.