Derivative of 1/x^3 from first principles

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In this video, I showed how to find the derivative of 1/x^3 from first principles. This process involves the use of basic binomial expansion using Pascal's Triangle

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How I love Dr. Newton’s presentation. Thank you.

jensberling

this was so great! I want to be a teacher and the way you go about teaching is so inspiring, thank you!

RowieFox

I'm now understanding CALCULUS because of you, , , , Thank you so much.

ummufaruq

Sir thank you very very very much, your video make complex things so easy to understand. God bless, and pls keep up the good work

BelemaJumbo-kwyb

I stop by your channel once in a while. If you watch some of the IVY LEAGUE university channels, you may notice that the smartest professors in the world keep their notes nearby if not in their hand. Teachers are not allowed to make mistakes like you have made several today. If you have experience in Japan and some other foreign countries, the teacher will keep their left finger on the negative sign to not forget to negate all calculations to the right. You will still be able to move your body out of the way so students can see your step by step solutions as you are working. Thank you for showing the Pythagorean Pyramid and the descending and ascending powers of the cubic expansion. Nice touch, cheers. THUMBS UP

Without proofs, carry the power of 3 to the numerator and add 1 to the power at the denominator, and negate the answer, done. But I like your solution better.

DuaneDonaldson

"Never stop learning, those who've stopped learning, have stopped living" 👏

tinotendajazire

Hey thank u for this video im from algeria, i like the way of ur teaching Dr
like u simplify the information
So thank you and good luck Dr Newtons

JijiJaja-fkpt

His smile is like "this gon be good"😂

bitspieces

I know the math but the video is refreshing. Thank you

aammiranda

I always love seeing the full derivation process, but I wanted to drop this pointer for those who may wish for a time saver:

Since 1/x^3 is the same as x^-3 I did a little trick; I dropped the exponent in front of the x, and then subtracted one from the exponent's value, and put this -4 in the exponent position. It only works with a monomial though.

f(x) = 1/(x^3) >>function to be derived
1/(x^3) >>rewrite as a monomial
x^(-3) >>move exponent down
-3x >>find value of new exponent
-3 - 1 = -4 >>put it all together
f'(x) = -3x^(-4) >>voila, your new derivative

that little trick can save you a lot of time, but it only works in a very specific situation

brrrayday

I used first principles to prove the power rule in the general case for positive integer exponents, and I’m hoping that this will help me do it in the general case for negative integer exponents.

StuartSimon

U ARE AMAZING
U SAVED ME
THANK U SO MUCH

SH-eopy

what if we have 1/x-2 how do you solve that sir

SiloloSililo

Sir u may say like if we have fraction over fraction then division on top is multiplication in bottom that easy

roythoppilchacko

Of course it is a good exercise the way you do it.But a more convenient way is to set y[x]= 1/x^3 .Then, x^3*y[x]=1,
and differentiation by the product rule givesy'[x]*x^3+3*y[x]*x^2 = 0 . A short calculation then leads to y'[x]=-3 y[x]/x = -3*1/x^4.

renesperb

Excellentl, Professor.
By the way, let us get the chance to learn how math knowledge is limked with Python algorithms or R algorithms.

JAMESYUN-et

You know you can also do common denominator on the fraction subtraction

Antagon

the final answer should be -3x to the power 2 innit ?

dionmaluleke-jzjb

... A good day to you Newton, I'm having your presentations as a part of my lunch time lately (lol); regarding this presentation it is indeed very smart/effective to multiply top and bottom by x^3(x + h)^3, thank you for this sort of advice. Busy day ahead today, so Newton also wishing you a pleasant day, and I'll be seeing you at the next challenging presentation ... Take care, Jan-W

jan-willemreens

help me solve this, from the first principle of differentiation, solve
f(X)=3

sethdarlton

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