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Review Blog. So for this blog I'm gonna review the product and quotient rules as well as the definition of a derivative. They are all pretty simple and everyone should know how to do these.

The first thing I will review is the definition of a derivative. This is what your are doing when you take a derivative. All you do is plug in your equation to the following formula:

lim [F(x+dx)-F(x)]/(dx)
dx->0

For example: Derive x^2+2

Plug in: (x+dx)^2+2-(x^2+2)/dx

Simplify: x^2+2xdx+dx^2+2-x^2-2/dx

Further Simplify: 2xdx+dx^2/dx

Factor: dx(2x+dx)/dx

Simplify and plug in 0 for dx: 2x

For the product rule: (x^2)(2x-1)

Derive the first, leave the second: 2x(2x-1)
+Derive the second, leave the first: +2(x^2)

Simplify: 4x^2-2x+2x^2

Further Simplify: 6x^2-2x

And the quotient rule: (x^2)/2x

[Bottom(Top Derivative)-Top(Bottom Derivative)]/(Bottom)^2

2x(2x)-(x^2)2/4x^2

Simplify: 4x^2-2x^2/4x^2

Further Simplify: 2x^2/4x^2

Further Simplify: 1/2

And thats it for this blog.