Derivatives

What is a Derivative?

• Almost every function has a derivative.
• The derivative of a function shows the rate of change (gradient) at any point on the parent function.

• The limit way of finding the gradient is called the first principles of a derivative, and it is roughly the equivalent of:

The Derivative Function

• The derivative function, also called the gradient function, is a function that shows the gradient of its parent function at any point.

• The notation dy/dx comes from "the change in y over the change in x", which is the definition of a gradient.
• The variables y and x can be replaced with different variables, especially when using the real-life applications of derivatives.

Differentiability vs Continuity

Sources

https://www.youtube.com/watch?v=iYUIl_ix4ng

https://calcworkshop.com/application-derivatives/derivative-graph/