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 primary rule as the chain rule.
Step 3: Break the problem up into two these two bite-size problems.
IN = SOMETHING and OUT = SOMETHING
Step 4: Take the derivatives of those two bite-size problems to find your DIN and your DOUT .
Step 5: Bring it all back together following the chain rule recipe: (DIN)(DOUT).