Differentiation : What is a derivative

In this video I introduce the concept of an derivative for the first time. I feel that in school etc., people are not told what an integral IS but rather how to compute an derivative. I think that is the wrong way to go about doing business, so here i go, enjoy!!
See also:
www.khanacadem...
tutorial.math.l...
• Finding Partial Dervia...

[@aaronthomas2381]

I have struggled with maths for as long as I can remember, I can't grasp the concepts, numbers etc are just like symbols to me. I've somehow managed to make my way into second year of a bachelors degree in Chemistry, and only after this video I managed to understand what a derivative is.

[@vagabond.studio]

7 years later it's still helpful

[@tkpmisai]

Thanks for a very clear yet simple explanation of differentiation... In my school days 17 years ago I really could not understand what are the meaning of all these.. Your explanation shed some light.... If only i could have access to this lecture years ago, I maybe can do better in the additional maths subject.

[@seanocallaghan5183]

Absolutely what I needed our teacher just shows how to differentiate but doesn't show us this essential information !

[@youspinmerightrounds]

To be honest, I'm not in position to record a video on partials at the moment.In their most basic form,computing partial derivatives is simple.Take the derivative of the whole function with respect a single variable,treating other variables as constants.Also, say a=f(x,y,z)=3xyz the partials are del-a/del-x=3yz and del-a/del-y =3xz and del-a/del-z=3xy. Then dy = (del-a/del-x)*dx + (del-a/del-y)*dy + (del-a/del-z)*dz (a VERY fundamental theorem in multivariable calculus).See the vid description

[@youspinmerightrounds]

I'm not sure what you mean. If you're asking is dy/dx = dx/dy then no because one means 'the rate of change of y with respect to x' and the other means 'the rate of change of x with respect to y'. now if you're asking is δy/δx = dy/dx then you're only half correct. d/d is called a 'total derivative' and δ/δ is called a partial derivative.If your function depends only on one variable it's a total y=f(x) but if it's y=f(a,b,c) then it's partial and we've δy/δa +δy/δb + δy/δc

[@sharonjuniorchess]

A great explanation. Key to this is grasping the idea of a slope which we call rise/run but even the egyptians knew about this although they measured run/rise. One useful application is in understanding how electrical components might behave and how those properties might be beneficial in certain applications. Once you know how to get the slope between two points we can bring those points together to find out what the tangent line is at any particular point on a curve. Geogebra is a great tool for creating curves and then plotting points on that curve that can then be varied and the slope calculated for those who are more visual learners. Once the geometry is understood the algebra can be applied. But there are still a few surprises in store and history can make this subject more entertaining as there are two approaches to this subject and we might have taken a wrong turn along the way which could explain why many people find this subject complicated or confusing.

[@Nothingmoretolosenow]

Hi Adam, Brilliant explanation. Its a shame that several people when teaching differentiation and integration dont do this. You identified this problem and uploaded a video. I hope several students and adults like me are getting benefitted. I hope you will comeout with more videos. Please try using a bigger board.

[@benjamintayaj]

Thank you for taking the time to explain the rationale of why we apply differentiation!

[@raik9536]

Brilliant work, thankyou for uploading this wonderful tutorial.God bless you kind sir^^, keep up the good work!!😁😁

[@antontonybekker]

Alternatively, can't you use delta x over delta y (I mean the Greek letter delta)?

[@santafucker1945]

good job mate..

[@arjitcool123]

please explain partial diffrentiation. well u have done a good job brother.

[@anoopsrana]

Very good video Dude......
Keep on uploading videos...

[@pranavmacha3597]

Thats a really good video to start up with differentiation, thankyou

[@mila868]

thank you! now i know that math has meaning

[@irispoonyt]

very heloful video !! simple and basic step by step

[@ziyadshafeek]

Very simplest of the explanation found so far !

[@anoopsrana]

Upload some examples involving Differentiation..... This video is very good by the way...

[@timclements2696]

Is d short for delta, the change in whatever variable you are trying to find out?

[@atklti3662]

Well done!

[@ramanjaneyulujagannadh2668]

What is difference between differentiation and derivative?? sirrrrrrr

[@qzorn4440]

good job. this explains the derivative in a PID steam controller. thanks.

[@giraldeauerone2003]

Thanks Bro helpes with ma mathsss need teachers like you in Fiji

[@Johnwantswater]

Have you got a video on how to.... for example
f(x) = 2x^n [using NX^(n-1) ] ? F|(X) ???? I know how to do it simply but have you got any with quotients and difficult to solve ones?

[@ShaharukhQureshiAP]

Awesome. Thanks.

[@hubomba]

Differential and derivative should not be interchanged. Derivative is defined as the rate of change of a function, while a differential is defined as the actual change of a function. Don't be ambiguous.

[@mahboubemaleki5256]

just perfect!

[@ahmadshajee3181]

thanks for keepingbit simple

[@anilkumargarada6589]

thanks for uploaded this video from this I got some concept

[@prabhnoorsingh7488]

Nice.. It was good.

[@eddiesanders2719]

Well taught! Thank you.

[@youspinmerightrounds]

Thank you!

[@Pharmaman100]

sometimes its like this { (dH/dP)t X dp (H is enthalpy,P is pressure and T is temperature)} ...i just can't get what is this??? Its like a differentiation and integration at the same time !!! its so confusing please help me :)

[@jayakrishnan26]

I watched this before teaching derivatives to my sister...

[@youspinmerightrounds]

Hi Abdullah, you're probably after something slightly advanced than this particular video. I'd be surprised if 'Thermodynamics 7 : Enthalpy' or 'Thermodynamics 35 : Thermodynamic Identity 1/2' do not answer your question

[@akashashen]

Velocity includes direction, not just time.

[@amzain09]

thanks alot....

[@lontongtepungroti2777]

super duper thakzzz dudez

[@LABE2504]

Thank you. Your video is very useful :-)

[@dadiziat4419]

what's rate of change ? please.

[@sakshidaga1499]

the video was really helpful! :D

[@asadalishahbukhari306]

thanks man this helped

[@hariram-jq9xb]

please tell me what is the tangent u mentioned above in the graph..please tell me briefly

[@youspinmerightrounds]

It's line which touches the curve at a single point only

[@MrYevin]

Thanks

[@popwavy]

you really have the talent :) thank you

[@ritwijkumar2170]

thanks forthis

[@srinivaspyla9742]

What is the meaning of " Derivative of any function with respect to a variable is equal to zero"

[@youspinmerightrounds]

This means that the function is not changing at that point. Remember, a derivative measures change - with respect to a particular variable. So df/dx = 0 means that f(x) isn't changing at whichever value of x set df/dx to zero.

[@srinivaspyla9742]

Thanks for your response

[@srinivaspyla9742]

Sir , if you don’t mind please tell me, what is the meaning of Xn=nXn-1

[@youspinmerightrounds]

Thanks for your question. It's not difficult to understand, but is difficult to explain in a CZcams textbox!!!
Xn is like f(x) where X is the function and it is a function of n. This notation is used for discrete functions where f(x) is usually used for continuous functions.
Anyway, consider a line where only certain values of x are permitted. E.g., x=10,11,12,13.. with the step size dx =1. Another way of writing this is to be more general and use a label 'n'. n1 is the first number, n2 is the second and so on, dn is always equal to 1. In this case n1=10, n2=11 and so on. But what if your're already at n4=13, then n3 is just n4-dn=12.
So Xn-1 is referring the value of X we had when we were at the previous value of n i.e., n-1. Your function is simply the current n multiplied by the previous value of X. So if your function makes the following if we start at X1=1: Xn=1,2,6,24,

[@srinivaspyla9742]

Thanks for your help.

[@asadshaikh8983]

nice

[@youspinmerightrounds]

it sure does

[@tombweisner]

Brill

[@devshishlaipubam8114]

didn't understand the way you teach in slope

[@RyNoDisTaNT]

This is horribly explained. In the integral video you said you would explain why:
y = 3x^2
dx / dy = 6x

[@vagabond.studio]

7 years later it's still helpful

[@antontonybekker]

Thanks