### The chain rule in multi-variable calculus: Generalized

Now we’ll discuss the chain rule for -nested functions. For example, an -nested function would be . What would be?

We know that

.

If is continuous, then

such that , which is equivalent to saying .

In turn

such that .

Hence, we have

Continuing like this, we get the formula

such that for all .

From the above formula, we get