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Finding derivatives using the limit defintion (also called the limit process), isn’t usually the fastest or easiest way to find a derivative, but you’ll probably have to learn it anyway. (And understanding it will help you understand derivatives, which will make it easier to learn the faster ways..)
To find a derivative with the limit definition, the basic strategy is always the same: Start with the limit definition and rewrite it with the function you’re trying to find the derivative for. The basic structure will always be: (the function with ‘X + H’) minus (the function with 'X’) all divided by H.
The next step to simplify and reduce until you can use direct substitution to find the limit as H approaches 0. How you do that will depend on your function, but there are some strategies that can help with different types of functions:
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