Chain Rule: Root of a quadratic: Find for .

If we define the a new variable, u, as the quadratic, we can simplify the problem and then apply the Power Rule and the Chain Rule:

Let . Then we have

We can use the Chain Rule here: . We shall calculate the factors separately:

, and

Now we can substitute these into the Chain Rule and get

Finally, we wish to express the result entirely in terms of x by using the definition of u above: