The formal definition of a derivative is
Stated simply, the derivative is an equation of a function that represents the slope of another line.
Here is an example of using the formal definition of the derivative to calculate the derivative of x to the second power.
Start with the formal definition.
Put f(x) into the formal definition.
Cancel out h.
Evaluate the limit.
The final answer is 2x as you can see. Fortunately, the derivative can be found using a shortcut called the Power Rule.
The Power Rule is a shortcut for calculating the derivative of a term. Note: The notation d/dx will be used to signify "the derivative of". Here's the equation.
Therefore, the derivative of 3x^2 would be