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.



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