Method: Product Rule Derivative

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.

• Roots or Radicals
• x’s on the bottom of a fraction.
• Trig functions raised to a power.

Step 2: Identify your primary rule as the product rule.

Step 3: Label one of your SOMETHINGS f , then label the other SOMETHING g .

It doesn’t matter which you label which.

Step 4: Break the problem up into two these two bite-size problems.

$f=\mathit{SOMETHING}$ and $g=\mathit{SOMETHING}$

Step 5: Take the derivatives of those two bite-size problems to find your $f\prime$and your $g\prime$.

Step 6: Bring it all back together following the product rulerecipe: $fg\prime +gf\prime$.