Concise and Practical AI/ML

Share

Explore

Mathematics Recap

Calculus

What are Involved?

Calculus by Newton-Leibniz, notably derivation. The Newton notation (use quote ‘) is neat and fast but harder to imagine, this book uses Leibniz notation (use d/dx) for solving the dynamic programming formula of backpropagation as the chain rule can be seen more clearly.

The

⁠

is read as derivative of f, the process of finding the derivative of a function is call derivation.

Derivative of a Function

Derivative of a function f is a function t which has results as the rates of change at all points of function f. Each result of t at x can be used as coefficient to draw a tangent line to the function f at x.

For example,

⁠

, the derivative of f is:

⁠

⁠

Basic Calculus: Derivation

Reference

⁠

https://www.mathsisfun.com/calculus/derivatives-rules.html⁠

⁠

Core Derivatives

Derivative of a constant:

⁠

⁠

⁠

Derivative of a line:

⁠

⁠

⁠

Derivative of a polynomial:

⁠

⁠

⁠

Derivative of a exponential:

⁠

⁠

⁠

⁠

⁠

⁠

More core functions are there but unused in machine learning.

Common Derivative Rules

Sum Rule

⁠

⁠

⁠

Difference Rule

⁠

⁠

⁠

Product Rule

⁠

⁠

⁠

Quotient Rule

⁠

⁠

⁠

Chain Rule (used when changing the variable that the derivation is taking respect to)

⁠

⁠

⁠

⁠

What are Involved?

Derivative of a Function

Basic Calculus: Derivation

Core Derivatives

Common Derivative Rules

Share

Want to print your doc?
This is not the way.

Try clicking the ⋯ next to your doc name or using a keyboard shortcut (

CtrlP

) instead.