Method: Quotient 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 quotient rule.

Step 3: Label your top SOMETHING hi , then label the bottom SOMETHING low .

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

$\mathit{hi}=\mathit{SOMETHING}$ and $\mathit{low}=\mathit{SOMETHING}$

Step 5: Take the derivatives of those two bite-size problems to find your dhi and your dlow .

Step 6: Bring it all back together following the quotient rulerecipe: $\frac{\left(\mathit{low}\right)\left(\mathit{dhi}\right)\mathit{–}\left(\mathit{hi}\right)\left(\mathit{dlow}\right)}{{\left(\mathit{low}\right)}^2}$.