The chain rule is a rule with regard to differentiating compositions of functions. In the following discussion and solutions the derivative of a function h(x) will be denoted by D{h(x)} or h(x). Most problems are average. Several are somewhat tough. The chain rule states formally that D{f(g(x))} = f(g(x)) g (x).

The chain rule can be used to composites of greater than two functions. To take the derivative of a composite of greater than two functions, notice that the composite of f, g and h (in that order) is the composite of f with g ° h.

The chain rule states that to compute the derivative of f °
g ° h, it is enough to compute the derivative of f and the derivative of g ° h.
The derivative of f can be computed directly and the derivative of g ° h can be
determined by applying the chain rule again.

## When to Use
the Chain Rule

Chain rule is used when there is just one function and it
has the power.

Eg: (26x^2 - 4x +6) ^4

Product rule is used when you can find Two functions

Eg: 56x^2 . (3x-10)

Here in the example you see there are 2 functions of x, one
is 56x^2 and one is (3x-10) so you must utilize the product rule.

Quotient rule is used when there are Two functions however
also have a denominator.

Eg: 45x^2/ (3x+4)

Similarly, you can find two
functions here in addition, there is a denominator so you must utilize the
Quotient rule to differentiate. However, if you are not confident with Quotien
rule then you can move the denominator up close to the numerator (with the
power of negative 1) and then utilize the Product rule, that's fine.