 Site Navigation                            Introductory Calculus: The Chain Rule
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 • There is another approach to this derivative which helps us with more complicated functions.

If we think of as made up of two functions, and , we could try to follow the power rule for the square.

• We get But if we start with and multiply by the derivative of which is we have: which is a factored version of our correct answer • Whenever and is another function of we can use this new method.
The Chain Rule Let's Practice:

1. If .

One advantage of using this formula is that we get an already (at least partially) factored version of the derivative.

1. In order to get the derivative, we first rewrite this as Now we apply the chain rule and we get 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.   Examples:            M Ransom

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