How do you find the derivative of the function: #f(x) = x^3 - 3x^2 - 1#?
This function involves the most commonly used rule for taking derivatives: the Power Rule. It states that whenever you have a power for a variable, that is automatically considered a product of the variable with the power being subtracted by one. Here is a general form:
For the function
Every time you have constants like
Thus by putting it together,
If you use the Limit Definition with
Solving for the equation gives you the same answer (though a long work process). The Power Rule and other rules for derivatives give you the shortcuts to solve for even the most complicated problems in using the Limit Definition.