Derivatives Rule! Even dogs can do it ...
NooNoo studying calculus

The Definition of a Derivative
Mathematics is the science of pattern ... let's look for some patterns ...
Let's use the definition to find some derivatives ...

The Derivative of a Linear Function
If then
Proof:
Example: Find the derivative of

The Derivative of a Constant Function
If then
Proof:
Example: Find the derivative of

The Derivative of a Constant Times a Function
Proof:
Example: Find the derivative of

The Derivative of a Sum of Functions
Proof:

The Derivative of a Difference of Functions
Proof:

The Derivative of a Power Function
Proof:

Example: Find the derivative of