Power Rule... How? (NancyPi)

HOW and WHEN to use the POWER RULE: If the given equation is a polynomial, or just a power of x, then you can use the Power Rule. For a term that's just a power of x, such as x^4, you can get the derivative by bringing down the power to the front of the term as a coefficient and decreasing the x power by 1. For example, for x^4, the derivative is 4x^3. If you have many terms added or subtracted together, and if they are powers of x, you can use the Power Rule on each term (by the Sum and Difference Rules).

NOTE: The derivative of a constant, just a number, is always 0 (that is the Constant Rule). Also, if you have a term that is a constant multiplied in the front of the term, like 2x^3, you can keep the constant and differentiate the rest of the term (Constant Multiple Rule). In this example, you keep the 2 and take the derivative of x^3, which is 3x^2, so the derivative of the term 2x^3 is 2*3x^2, or 6x^2.

ANOTHER NOTE: You can use the same power rule method for fractional or negative powers, but be careful... for negative powers, it works as long as x is not 0, and for fractional/rational powers, if the power is less than 1, your derivative won't be defined at x = 0.

Editor: Miriam Nielsen of zentouro

Director: Kristopher Knight

[fizazaman]

You're the best maths teacher I've ever had...and I've studied fully at both a private and a grammar school. Keep it up! I recommend you to everyone :)

[NikachuMTG]

Hi, Nancy! I remember you from mathbff. 4 years ago you single handedly helped me get an A in pre-calculus and I followed it up with an A+ in calculus. Your videos are beyond helpful because you deeply understand how to convey mathematical concepts to people learning.

[cmaanlife]

I just wanted to take the time to say thank you because you helped me much throughout the years!! I just took my last college lvl math class at UMD and I passed with a 92% thanks for uploading these videos to youtube when you don't have to. It really helps alot of us out who may not have the best of teachers or the learning environment for math at some colleges just isn't personal enough.Anyways you helped me more than you can imagine, so thanks again.

[Plasmon]

I got distracted there for a bit but watching the video 3 times helped memorize everything. Now I'm ready to use the power rule. Next lesson.

[NiHaoMike]

The power rule also works on constants! Think of a constant as being multiplied by the zeroth power of x, so that on taking the derivative, the zero is pulled down and the whole term disappears. (Not that there's a reason to use it but it's always good to see mathematical rules staying consistent.)

[cjeelde]

I found a video from your channel thanks to recommended videos cuz I've watched many math/science videos - and wow, I love you and your videos! You explain everything so good, you write so good, and love those 'speed-ups" and how it's filmed/recorded. Wish I had your videos to watch when I had math in school, but as it is now - your videos are perfect to refresh the memory and I actually also learn some new stuff. You're an amazing math teacher! BIG love to you ❤️❤️❤️❤️

[DecafMathASMR]

The ending is the cutest thing ever! hahaaa nice job

[ChrisyAri]

Hello Nancy;
I'm Prof. Cris from the Matelok Channel. A pleasure to always watch your videos .. I really like your style of making the videos .. Do you use a glass or something like that? ...

[Ryan-pgmg]

Hi Nancy! Thank you so much for all of your videos -- you explain everything so well! Can you make videos on sequences and series? I really struggle with partial sums and pretty much all of the tests to determine convergence etc.. I feel like sequences and series are a tough topic across the board, so a series (ha) of videos on this topic would probably be helpful to a lot of us.

[David-fgnu]

Just in time for my calculus final tomorrow!😍 I love you!

[jwo]

Nancy, I do not know how many people who watch you realize that you are teaching extemporaneously and to an extremely wide audience. This shows your grasp of the subject matter and your grasp of how to speak to people about complex subjects without talking down to them and without talking over them. It is obvious to me that you are a disciplined person who cares about others. A rare and desirable set of character traits.

[tannerbarcelos]

Doing these are actually fun lol. Math is a lot more fun, and intuitive, when you just take a step back and really try to understand it. Luckily, Nancy I here to save me in class and everyone!

[johncarlomanabat]

I learned how to solved power rule and I learned how to love the teacher

[thedavegoodman]

updated videos! And you're much more relaxed now. high five!
I need to use calc again and couldn't find the mathBFF channel, I'm glad you're still here. high five again!

[KisemboPhysicsAndMath]

The power rule. Wow, been planning calculus videos on my own channel. I hope one day I'm able to adopt your production quality, it's soo next level. Your channel is such an inspiration. Great work you're doing Keep it up Nancy

[laancedance]

I'm learning about derivatives right now, this video was quite helpful

[cmu]

Thanks Nancy!!! This was really helpful for my Cal 1 class.

[Ashna-ss]

Thank you so much.😀
Your videos are short and great and it's never boring. You are a perfect math teacher . 🙂
This is really a topic that i didn't understand from school but i understand it now.

[sdzztdcsad]

This is what I learned at the beginning of this year, this is pretty simple

[AynRand]

Love you Nancy. Fractions in derivatives Drove me nuts.