Chain rule

In differential calculus, the chain rule is a way of finding the derivative of a function. It is used where the function is within another function. This is called a composite function. 
More specifically, if formula_1 equals the composite function of the form:
where "g" is a function differentiable at "x" and "f" is a function differentiable at "g"("x"), then the derivative of formula_1, written as formula_4, exists, and is equal to
Steps.
1. Find the derivative of the outside function (all of it at once).
2. Find the derivative of the inside function (the bit between the brackets).
3. Multiply the answer from the first step by the answer from the second step. This is basically the last step in solving for the derivative of a function.
For example,
In this example, the cubed sign (3) is the outside function and formula_8 is the inside function. The derivative of the outside function would be formula_9, where "x" is replaced by the inside function. The derivative of the inside function would be 2"x", which is multiplied by formula_10 to get formula_11. 
Proof.
The very definition of a derivative is formula_12. 
With this knowledge:
formula_13 must be true, which can also be written as formula_14.