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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