Note that in this lesson we show examples, but not any proof
that the formulas for the product
and quotient rules are correct.
A Modified Power Rule (The Chain Rule):
- If , then after first multiplying
We can then find the derivative by
- If .
One advantage of using this formula is that we get an already (at least partially) factored version of the derivative.
In order to get the derivative, we first rewrite this as
Calculate the derivatives of each function. Write in fraction
form, if needed, so that all exponents are positive in your final answer. Use the "modified power rule" for each.