Derivatives

One of the most important calculus concepts to learn is derivation.  Here I will show you how to calculate some simple derivatives.  The derivative looks like this and can be read as “derivative with respect to x” so if you have a function and you are supposed to perform then you are going to be taking the derivative of the function “f” with respect to all variables “x”.

If n is a positive integer, this is your theorem:

let’s apply this to our equation .  Our derivative is looks like this to start where n = 1 because 5x is not raised to any power.

The first derivative will be represented like so:

or

Our equation is now equal to a constant.  If you take the derivative of ANY constant, the result is Zero.  So here

Let’s make this example a little more realistic, our new equation is

each piece of the equation loses 1 order ( second order), keeping in mind that the 3 was a constant and is now zero.

we can continue all the way to zero.