## Chain Rule Formula

The chain rule is used to help perform more complicated forms of differentiation. We use the chain rule when there is a function within a function. This may seem a little complicated but after a bit of practice it is easy to identify.

The formula for the chain rule is provided in the formula sheet:

At first glance it may seem a little confusing but the basic idea is that we separate out the function within a function and differentiate them separately.

## Chain Rule Example

For example from the 2014 exam 1, Question 1b. Find f'(1) for:

**Step 1 ** We convert the function into a more friendly looking form, we will also replace our notation of f(x) with y so that our process will resemble the formula provided. There is no harm in doing this as long as when you write your final answer you use f ‘(x) instead of .

**Step 2 **This is the hardest part of the process as we need to choose which part of the function to set to u in order to simplify our differentiation. For most functions it will just be our bracket terms, for example:

This also gives us:

**Step 3 **Find ** **and

This is now just straightforward power differentiation.

**Step 4 **multiply together the two terms to find

**Step 5 **we substitute in

That completes the differentiation part of the question and we have converted it back to the form of f'(x). Now we just need to find f'(1) by substituting x = 1 into this function

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