In this video we will learn HOW the MAIN DERIVATION RULES are OBTAINED and it is that, when we learn to DERIVE we use the FAMOUS DERIVATION RULES, however, many of us made use of these RULES without really understanding what each of the results we obtained meant, in this series of videos we will EXPLAIN IN DETAIL how the main derivation rules are obtained through the use of the definition itself. This is just one of the first videos that we will dedicate to talk about DERIVATIVES, so if you find this content valuable and useful, you can support me by SUBSCRIBING TO THE CHANNEL, COMMENTING AND SHARING Thank you for your attention :D #derivatives #differentialcalculus #differentialcalculus ************************* CHAPTERS: 00:00 Motivation 00:50 Introduction 01:32 Formal definition of the derivative 06:20 Derivative rules 06:47 Leibniz and Lagrange notation 08:28 Derivative of a constant function 12:16 Derivative of the identity function 14:33 Derivative of function f(x) = kx 17:12 Derivative of quadratic function 19:28 Derivative of function f(x) = x^n 24:54 Derivative of the sine function f(x) = senx 28:43 Derivative of the cosine function f(x) = cosx 30:45 Summary of elementary derivatives 31:20 Trigonometric derivatives 32:21 Preview of the next video 32:48 Thanks and farewell *************** You can support the making of more videos like this by being a MEMBER OF THE CHANNEL, with your help I will be able to make more videos until I complete a playlist with university mathematics from the most basic to the most complex through animations! The creation of these videos takes me quite a bit of time. If you want to help me continue creating content on YouTube, I invite you to support me on PATREON and ACCESS EXCLUSIVE BENEFITS: / bluedot96 Follow me on Twitter: / bluedot96 Follow me on Facebook: / bluedot1196 Follow me on Instagram: / pauloch96 I RECOMMEND THESE VIDEOS: WHAT IS THE DERIVATIVE?: • The DERIVATIVE changed EVERYTHING 🚀 WHAT is... WHAT IS THE INTEGRAL?: • What is the INTEGRAL? MEANING of... WHAT IS A FUNCTION?: • A function is NOT A MACHINE WHAT... FUNCTIONS FROM SCRATCH: • WHAT is A FUNCTION? ▶ CART PRODUCT... LINEAR FUNCTION: • What is a LINEAR FUNCTION? ▶ GRAPH... QUADRATIC FUNCTION: • WHAT is a QUADRATIC FUNCTION? ▶ Com... FUNCTIONS OF TWO VARIABLES: • WHAT is A FUNCTION OF TWO VARIABLES?... THE INTEGRAL FROM SCRATCH: • This THEOREM CHANGED EVERYTHING 🚀 WHAT... DIFFERENTIATION : • This IDEA OF NEWTON FOUNDED the BASIS... RULES OF DERIVATION: • The UNKNOWN side of the DERIVATIVE 🧐... WHAT IS CALCULUS?: • Why did CALCULUS CHANGED EVERYTHING? ... WHAT IS A LIMIT?: • A FANTASTIC INTRODUCTION to LIMITS... THE LIMIT EXPLAINED IN DETAIL: • WHAT is the LIMIT of a FUNCTION? ▶OF... LIMIT PROPERTIES: • WHAT IS BEHIND THE FAMOUS PROPERTIES... WHAT IS OPTIMIZATION?: • Why SHOULD YOU LEARN OPTIMIZATION... WHERE DO SIN, COS AND TAN COME FROM?: • REALLY UNDERSTANDING WHAT SIN, COS... UNDERSTANDING SIN, COS AND TAN: • UNDERSTANDING THE SIN, COS AND ... ***************************************************************************************************** The animations in this video were made with Manim (Mathematical animation), a library for Python created by Grant Sanderson (3Blue1Brown). Personally, I find it to be a very useful tool to be able to better explain many concepts in a visual way. If you are interested, here is the link to the Manim library for Python: https://github.com/3b1b/manim Without further ado, thank you for your attention and see you in the next video!