A Derivative is the slope of the tangent line of a function. It is also called
the rate of change. Derivatives are used to find many different things and
there are many different formulas used to find them. Below is the Definition
of a Derivative
. It is the key method of solving these problems. (y=f(x) is a
function for these problems):

The Definition of a Derivative:

There are many different types of formulas inside the main defintion that make
finding the derivative easier. Below I will show examples of the Power Rule
and the Basic Chain Rule:

The Power Rule:

This formula is pretty easy to understand if you just take a minute to look at it.
Basically, its the power that you raise (x) to times (x) raised to the original power
minus 1. This creates a very easy shortcut as opposed to possibly having to write
out a long formula for the Definition of the Derivative if it power was more than
squared.

The Chain Rule:

This new rule is tricky in the sense that we're replace (x) with (u). The reason
behind this is that in this formula, (u) equals an equation, sometimes a polynomial
that contains the variable (x), and it's much easier to classify it as (u). When looking
at this, it becomes simple if you take it apart. The function of (u) raised to the (n)
power is equal to (u) times the function of (u) raised to the (n) power minus one
times the derivative of the function of (u). Basically this is the power of the power
rule. Later on I will show some examples of this formula at work to better explain it.