The derivative is a VERY IMPORTANT concept in Calculus, but what is there beyond calculating derivatives by memorized formulas and without really understanding them? In this video you will understand the fundamental bases to build the concept of the DERIVATIVE and you will also be able to know its usefulness and why it is so important. #derivatives #differentialcalculus 00:00 Motivation 00:42 Introduction 05:05 What is the slope? 07:46 Slope of a line 09:17 Speed ​​as the slope of a graph 10:39 Intuitive idea 13:30 Formal definition of derivative 17:14 Derivative of the quadratic function 19:52 Interpretation of the derivative 21:20 CdeCiencia moment (Tribute to Marti from CdeCiencia for inspiring me to create content) 22:23 Farewell and thanks 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 MUSIC: Kevin Bryce: / @kevinbryce VIDEOS: https://pixabay.com/es/videos/ 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 i... 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!