Derivatives... How? (NancyPi)

For

What is the derivative? It's 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), but the fastest way to find the derivative is with shortcuts such as the Power Rule, Product Rule, and Quotient Rule:

1) 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. 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.

2) PRODUCT RULE: If your equation is not a polynomial but instead has the overall form of one expression multiplied by another expression, then you can use the Product Rule. The Product Rule says that the derivative of two functions multiplied together is equal to the first function times the derivative of the second function, plus the second function times the derivative of the first function.

3) QUOTIENT RULE: If your equation has the overall form of one expression divided by another expression, then you can use the Quotient Rule. The Quotient Rule says that the derivative of one function divided by another (a quotient) is equal to the bottom function times the derivative of the top bottom minus the top function times the derivative of the bottom function, all divided by the bottom function squared. This is true as long as the bottom function is not equal to 0.

[arianahouman]

Why go to college and get confused for hours when there's a free 15 minutes video that explains everything? We need more teachers like you!

[mcorona]

I took calculus last semester and had to drop it, too complicated. Gave it another go and stumbled across Ms NancyPi and I'm killing it with a straight A. She helped me understand in less than 20 minutes what I couldn't over an entire semester. Just simply awesome

[erichomsy]

i figured it out. when she's filming she writes the equation out so its legible to her and then mirrors the video in post. genius

[juliomontenegro]

Im taking Calculus in college right now and after class I basically re-teach myself using your videos thank you so much!

[yourverdict]

Thank you so much for posting again you literally got me through highschool math....im in foster care and ended up going to 6 high schools in4 years....literally you are the only reason I passed math

[RachelHannah]

Like honestly, WHY aren't experienced college professors as incredible as teaching as this young student!?

[aleynan]

I seriously didn't think I'd ever understand this based on the way my professor taught it but the way you explained it is so simple. Thank you!!!

[waqasshinwari]

Started studying mathematics after 15 years for my PhD economics courses, and your videos are truly the saviors for me. You explained in a brilliant way, thumbs up.

[juang.]

my professor uses your videos to make sure we understand the lecture he just gave. Thanks for helping with my H/W.

[caseses]

When I graduate from my MSc, I legit am going to acknowledge your contribution. Thank you for saving so many tests

[koxukoshu]

"you probably should do that... because reasons"

truly

[timbausch]

I found myself drowning in a machine learning course and would have been dead in the water without your videos. Thank you so much for literally the best explanations and demonstrations I have ever seen. I can't wait to watch the rest of your videos to get caught up with math again! Thank you!! :)

[sophiedallimore]

You're one of the first people to make calculus make sense to me, thank-you so much!

[stephanieirissapno]

Omg i was like absent minded when my teacher was discussing this and it was so boring, his voice was like a lullaby. Thankyou so much for this i completely understand it now

[stangabay]

Ok, I'll say it because we're all thinking it. Smart and beautiful! Thank you for taking the time to show us how to do derivates in a
very simple and understanding way! No math-ese. You speak our language! Thanks, again!! :)

[DonDOSS_]

who can explain in so much simpler terms . you are amazing in teaching and beautiful as well .lot of bonuses in one shot . thank you .

[robynm]

Actually going through cal 1 right now so much appreciated.

[jessemclaughlin]

You're a walking angel. Thank you so much for your videos. I love how you are able to dummy it down. I've literally gotten thru calculus off of just your videos.

[tolineee]

Literally wish you uploaded these before I failed my class two year ago, you are so composed and make it really easy! I took the class again this year and did really well on my last exam. Thank you never stop with these.

[seaknightvirchow]

I am retired. i took calculus 45 years ago and I have forgotten most of it. I have decided to relearn my basic math beginning with algebra and trig. These videos, even calculus, are bringing back so much of what I had forgotten. You are a very good teacher. Somehow these concepts are now easier to understand than when I first encountered them and though part of it is dusting off the once learned material, I think it is also due to how you explain things so clearly.