The Chain Rule for Derivatives in Calculus - [1-5]

In this lesson, you will learn how to take derivatives in calculus using the chain rule. The chain rule instructs us on how to take derivatives of nested functions, or functions inside of functions. The procedure is that we take the derivative of the outer function, then take the derivative of the inner function, then multiply the results. Here we practice taking derivatives using the chain rule.
More Lessons: www.MathAndScience.com
Twitter: / jasongibsonmath

[@paulatlin9067]

Who needs to attend college when we have the best professor (Jason) teaching us! Thanks Professor

[@frankepala]

Frank

[@DandoBorusu]

I dropped out of engineering 8 years ago. this dude would have saved my career.

[@cluelessinky]

There are instructors who know the stuff but can’t teach the stuff. And then there are instructors who don’t know but fake it. This instructor knows the stuff and knows how to teach it. He is changing the world of teaching for the better. Thank you

[@ramanivenkata3161]

Excellent. Very well explained

[@kevin-gg8ir]

You, sir, are literally helping me see the bigger picture. Thank you! 👏

[@MathAndScience]

Happy to help!

[@niyonkuruidrissa2346]

Much respect 🙏💯

[@pinakgohil]

Oh how can I forget this! Its part of my studies. 🙂

[@drumtwo4seven]

Nice 👍 Haven't taken calculus yet... have only gone thru trigonometry and college algebra. But wish I could 👍

[@MathAndScience]

You can do it!

[@yuusufliibaan1380]

Thanks 🙏

[@MathAndScience]

You’re welcome 😊

[@hemrajue3434]

Find the derivative of log x^2. 1) y=log x^2 Y'=1/x^2 ×2x=2/x. 2) y=2log x Y'=2/x. 3) y=log x+log x Y'=1/x+1/x=2/x.

[@qualquan]

"Nested" or 'Composite" or "Function of function" can be better described by the concept of SEQUENTIAL Independent Variables (IVs) e.g Primary, Secondary or higher IVs. Each higher IV is often called the "Inside Functions"(IF). Additionally each sequential IV or IF has it's personal Dependent Variable (DV) often called the "Outside Function" (OF). We begin differentiating sequentially the highest DV or OF and its IF by its preceding IF and continue till all the higher IFs are differentiated by their preceding IF. If any higher IF is not explicitly, meaning numerically, differentiable by it's Preceding IV then the higher IV is called an "Implicit" Function. The Chain rule is applicable whether the Higher IV is explicitly (numerically) differentiable by the Preceding IV or not. Substituting "U" or ""M" for the higher IV or "inside Functions" makes life much simpler and explanation clearer but unfortunately he does not utilize the "U" substitution technique. His examples are done well but he has trouble with definitions and to some extent explaining the underlying logic of why we MULTIPLY by the derivative of every Inside Function (IF) rather than add or divide)

[@user-yp5ep1tm8o]

Makes maths simple

[@hsjwvs]

Hello sir, if i did the formula getting 3u² • 6x + 5, why should I not distribute 3u² to every term?

[@dorischoo]

I just cannot imagine how some people ‘Jason’ can figure out this nested function. Unable to even grasp it.

[@fahimkhalasi4115]

i like calculus but calculus is my major . i am doing both single and multivariable calculus

[@johnserge3930]

This is interesting but not quite so easy.