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: Make sure you have both the original function, , and the inverse function, .
-
If you missing one of the equations, you can find the other through an algebra.
-
No matter which one your given to start with, you can find the other through this process.
-
Swap the position of
x
and
y
in the equation you are given. Keep in mind that or are the
y
.
-
Resolve that new equation for
y
. In other words, get
y
alone on one side of the equals. That result is your other equation.
Step 3: Find the derivative of , the original equation.
Step 4: Construct the piece of the inverse derivative rule.
Step 5: Bring the pieces together following the inverse derivative rule, .