Step 1: Simplify and look for algebraic rewrites.
This is your new version of Option 1 from limits. This means it is the first thing you will always want to do before you start actually applying a derivative rule. You must ensure that the equation is ready to have a derivative taken.
Step 2: Identify your derivative rule as including the base case .
Remember as soon as what is inside the power of a is more than just your basic x , the problem becomes a chain rule process.
Step 3 (If it has more than just an x ): Run the standard chain rule process with whatever replaced your basic x as the inside piece.
Step 3 (If it has just an x ): Apply your specific trig function’s special case rule.