# Power Rule… How? (NancyPi)

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Published on December 12, 2018 by

MIT grad shows how to find the derivative using the Power Rule, one of the derivative rules in calculus. It is a shortcut for taking derivatives of polynomial functions with powers of x. To skip ahead: 1) For HOW and WHEN to use the power rule, skip to time 0:22. 2) For how to use the power rule when you have a FRACTIONAL or NEGATIVE POWER, skip to 5:22. For my video on the other differentiation rules, PRODUCT RULE and QUOTIENT RULE, skip to https://youtu.be/QqF3i1pnyzU?t=456 Nancy formerly of mathbff explains the steps:

For how to differentiate using the formal LIMIT DEFINITION of the derivative instead, jump to https://youtu.be/-ktrtzYVk_I?t=628

Support Nancy on Patreon: https://www.patreon.com/nancypi
Follow Nancy on Instagram: https://instagram.com/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.

The derivative is a function that gives you the instantaneous rate of change at each point of another function. You can calculate the derivative with the definition of the derivative (using the limit, see https://youtu.be/-ktrtzYVk_I?t=628), but the fastest way to find the derivative is with shortcuts such as the Power Rule, Product Rule, and Quotient Rule.

For my video on the CHAIN RULE for finding derivatives, jump to https://youtu.be/H-ybCx8gt-8

For more math help and videos, check out: http://nancypi.com

Editor: Miriam Nielsen of zentouro

Director: Kristopher Knight
https://kristopherknight.com

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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? …

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• 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.)

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• Angel Nancy,
Thanks for teaching me Power Rule.
Please make videos for the following topics:
How to find Maxima,minima and points of inflexion by using Differentiation.
HAVE A NICE DAY!

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In future videos could you expand upon the material already provided by MIT? More intermediate and advance topics of computer science… and since you’re a self proclaimed math nerd, you could focus on algorithms and how they work (instead of how to implement them). You could do a video on gradient descent as an example or any of the many sorting methods and the maths behind them.

Another suggestion would to be to take a page from the youtube channel “Socratica” and provide short clips on studying techniques, job/internship hunting/interview techniques, and anything else that helped you get through MIT’s rigorous curricula. This would help increase your upload frequency, while not taking up too much of your time that is normally spent on your longer videos.

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This book is called the Qur’an and I believe it is the only book in the world of this kind…
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It should be interesting for every mathematician…

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Can you please make a video on HOW TO FIND SOLUTIONS OF ORDINARY SECOND ORDER LINEAR DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS.
It would be really helpful.
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interesting video
ps
you are beautiful

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can you PLEASE make a set of videos on statistics and probability? The topic is simply killing me and I sure could use some help.
By the way, I like how all the formulae appears right next to you on the screen 🙂

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• Universal Repulsion – a new fundamental force.

Similar to universal gravitation force between matters, there is an universal repulsion force between line of sight electrons on the surface of matters. Without gravitation, we cannot orbit the Sun. Without repulsion, Sun light cannot reach us.

Because electrons are on the surface of all matters, and because line of sight electrons are constantly repelling each other with Coulomb’s force F=Ke x ee/R^2, therefore between the surfaces of matter A and matter B there exists an universal repulsion force F=Ke x aebe/R^2. In the equation, a is the number of line of sight electrons on the surface of mater A, b is the number of line of sight electrons on the surface of matter B, R is the average distance.

This universal repulsion force is always existing at any distance, therefore line of sight electrons are constantly connected by this force at any distance,  therefore they can share their kinetic energy instantaneously at any distance.

This universal repulsion force is the conductor of light energy in the vacuum space between stars and planets. Light energy is instantly shared between line of sight vibrating electrons on the surface of the Sun and electrons on Earth outer atmosphere, then it becomes light wave and traveling in the air at light speed C.

This universal repulsion force is the conductor of light between things you see and your eyes. Due to air in between, light speed is C.

This universal repulsion force is the conductor of EM wave between antenna and receiver. Due to air in between, EM wave speed is C.

Due to the existence of universal repulsion force, all star lights reach Earth outer atmosphere instantly, become light wave traveling in the air at speed C.

Sun light takes 8 minutes to reach us is mistaken. Time delay in space communication is impossible.

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Use MIT trillion frame per second camera to measure light speed inside of a vacuum glass bottle, we can prove light speed in vacuum is infinite.

Light only exists in air, water, medium/matter. There is no light in vacuum space.

Energy instantly teleported from the Sun to Earth outer atmosphere. Due to the existence of universal repulsion force between electrons on the sun and our outer atmosphere.

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They were both wrong.

• Make more calculus videos plz

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• could you do a vid on Consecutive integers?

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• Do exponential graphing and inequalities or finding the maxama and minima within a domain .

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• Kindly make a video on maxima and minima of function of two variable please solve this example
x^4+4x^2y^2-2x^2+2y^2-1

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• Chinese viewer has entered chat

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• 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.

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I mean : you seem to be sited behind a glass and write letters and characters in inverted ? Or maybe there is a trick ?
Can you explain us how you realise this kind of video ? I’m beginning teaching to youtube too, and this way of presenting is very very cool !

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I’m trying to learn *MOVE*

• I am curious about how she wrote. It seems that there is a transparent glass whiteboard, on which she wrote, between the camera and her. However, if she stood on the other side of the glass whiteboard, then everything that she wrote would be reversed/mirror, which is very difficult for the writer. Did she really do that? But if she wrote normally, how to make the formulas mirror back in the video? After all, you can see that the formulas covered her left hand, which means she should be in the back.

Any ideas?

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Can you make a series of video about matrix 0 to 100?
Thanks a lot

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• HI!
Can you solve the standard questions, from algebra , limit, integral

• Actually this is mirror effect. Actually she is not writing right to left but this is the mirror effect. She is actually sitting left of her and right of us

• Writing backwards is the impressive part.

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• Tip*** To minus one from a fraction, just keep the denominator on the bottom and for the top subtract the denominator from the numerator. Example 4/3-1 = 1/3

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• How do you write so good backwards!? 🤯🤯🤯

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• Thank goodness for this video! I slogged through two hours of the original method for a 60%, but this makes it easy, and I never thought id say this, fun!

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I wish i have a chance to meet u

• Had she been my math teacher, I convinced I would have paid much closer attention in class.