What is Differentiation ? | Concept of Differentiation in Mathematics 

@@MrStrangerr2002 thank you so much for the wonderful encouraging feedback!! Hope to continue making relevant and useful content !! 😊😊👍👍

Thank you so much for the wonderful feedback... delighted to read your comment...keeps me motivated!!😊😊👍👍👍

That's great.... Really happy that you found the video useful..thank you so much for the appreciation !! 😊😊👍👍👍

Thank you so much for that awesome motivating feedback ! Really means a lot!! Very happy to be of help 👍👍👍👍

Not sure how did you calculate speed at 11.00001 secs.If you calculate it it will be 107.80004 m/s and not 110 m/s?

@@arunahuja1839 hello,can u explain how u have got the speed value as 107.80004 m/s ?

Yes 100 percent

​@@arunahuja1839 he is true if y= 4.9t^2 then dy/dx will be 9.8×t^2-1 = 9.8×t ,, t taken as 11 then we get 107.8 where u got at 11.01 so there might be wrong calculations done by u ( channel owner )

@@fashionista_2009 thanks a million for that awesome feedback!! Motivates me a great deal to continue making relevant content!! 😊😊😊👍👍👍

@@EnjoyMath You desrve alot of subs Respect for you beautiful young lady ❤️🔥

@@fashionista_2009 thank you so much!! 😊😊😊

Thank you so much for the wonderful and motivating comment!! Really humbled and happy to get this appreciation from a teacher in the same field🙏🙏🙏 The idea of humour is really brilliant....I now recall my teachers too making the class more enjoyable by cracking jokes....yes, will definitely try this out ..thank you so much for the suggestion 🙏🙏 Really good content on your channel sir👍👍

That's so good to hear!! I am really glad the video has helped u understand differentiation better...thanks so much the motivating feedback!! 😊😊👍👍👍

Thank you so much for the wonderful comment . Glad that you found the video useful🙏🙏👍👍

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@@EnjoyMath maam can you make a similar video for integration

@that.guy.09 yes , will try my best...will take some time,but will definitely make it...thanks a lot for the suggestion 👍👍👍

Thank you so much for the wonderful feedback!! Really happy that you found the examples and explanation easy 👍👍👍

Thank you so much for the wonderful comment.... really delighted to read your feedback!! Yes indeed, differentiation is a bit different from what we have learnt till now...hence perhaps it takes a bit longer for us to grasp the concept....but it's amazing how the great mathematicians developed this branch called differential calculus....it's really an ocean...

So nice to hear from you again.... thank you for the feedback!! Can you just give me the timestamp of the equation you did not understand? I will then try to explain it...

Thank you so much for the wonderful feedback, really means a lot!! Yes, will surely plan more such videos in future, if you have any topics in mind,pls do share👍👍👍

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Hello.I am sorry I am unable to read the script. Pls let me know the translated comment .Thank you 👍👍🙏

@@EnjoyMath God reward you

@@inmathsstar Thank you so much for this wonderful message!!! What a nice blessing to start the new month. Thanks a lot 🙏🙏🙏

@@EnjoyMath you welcome

Thank you so much for the wonderful comment....glad to know that you found the video useful!! 😊😊👍👍

Yes,you are correct....I have taken approximate value....have mentioned in the pinned comment 👍👍

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Thank you so much for the wonderful comment!! Really means a lot !! very glad to be of help 👍👍👍😊😊

Thank you so much for the wonderful comment... really keeps me motivated!! This equation is from the equation s= ut+1/2at²...here u=0,hence we got u=1/2at², here a=g=9.8, therefore u= 4.9at²,pls let you know if you have any questions...

@@EnjoyMath thank you Priya and greatly appreciate your response !

@rajithajay7595 most welcome!! 😊😊

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@@UsernameXYZ947 thank you so much for the appreciation!! 😊😊👍👍 s=ut+1/2at², where s is displacement, a is acceleration due to gravity, u is initial velocity.... Here, u=0, a=9.8, Therefore, s= 9.8t²/2 s= 4.9t² Pls let me know if you have any questions...

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Thank you so much for the appreciation!!! Yes, I have unwittingly rounded off the distance value at time= 11.00001 s. More accurately it should be 592.901078 I will pin this as a comment so that the confusion is cleared. Very Sorry to have created confusion for you

Really??? I will take it as a compliment!!! 😊😊

Thank you so much for the appreciation!! Really means a lot....yes, i accept the points you have mentioned...thank you for the feedback,will keep them in mind while making future videos 👍👍👍👍

Thank you so very much for the wonderful comment and support 🙏🙏👍👍

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Really happy that you have understood the concept ....thank you so much for the wonderful comment!! 😊😊👍👍

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@@EnjoyMath hay in which class are you studying currently

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Velocity defined as the rate of change of displacement....so v= ∆s/∆t Now, for instantaneous velocity,the ∆t is very small or almost close to zero....still we have to find ∆t.....that's where differentiation comes to picture because limit ∆t tends to zero, ∆s/∆t = ds/dt Pls let me know if you have any questions...

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Thank you so much for the encouraging feedback, very happy to be of help 👍👍👍

Thank you so much for your valuable feedback🙏🙏 It feels really nice. Your suggestion is very good sir. I actually started a Hindi youtube channel last year but have hardly put any content there due to time constraints. I would love to make hindi videos too..but I am not sure if viewers would want hindi and english videos in the same channel. But I will seriously think about your feedback sir . May be I can upload my english videos with hindi voice over. Pls let me know your opinion sir about this and thanks once again for sharing your feedback .🙏🙏👍👍

@@EnjoyMath Dear Ma'am, I am from South India, I would propose that using English language would be helpful for more people rather than using regional language. Thanks for the great content and your dedication ma'am!

Thank you so much for your appreciation. It's really very motivating. 🙏🙏 And thanks a lot for your valuable feedback. Yes your point is also very valid. Will keep that in mind.👍👍

Most welcome!! really so happy to be of help!! 😊😊👍👍

As per the calculations in the example, 593.9785-592.9= 1.0785 That is divided by the time interval 11.01-11= 0.01 1.0785/0.01= 107.85 m/s I think actual instantaneous speed at a given moment is same...now the question is how accurately we capture its value....if we keep the time interval large , our instantaneous speed will be less accurate,while if we keep the time interval as close to zero as possible, we will get instantaneous speed more closer to the accurate value....pls note in the example, in all the cases,we are only discussing about instantaneous speed at the same moment... Pls let me know if you have any questions...

@@EnjoyMath Thank you for your quick reply... I don't have any questions regarding this. I tried to give my view... Nothing more than that.... Thank you again...

@@bhavi9891 really appreciate your out of box thinking.... curiosity about things is the best way to learn and understand 😊😊👍👍

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Yes sure, which topics of class 12 math you want videos on ? 👍👍👍

Most welcome!! Really happy that you found the video useful 👍👍👍👍

Thank you so much for the appreciation!!! 👍👍👍 Well, in one line, one may say that differentiation is rate of change of a quantity with respect to another quantity.....

@@EnjoyMath thanks

Thank you so much for the wonderful wishes !! 😊😊👍👍

Hello, h is a variable whose value is not zero,but is very very close to zero or tending to zero. In the video example, we define velocity as the change in displacement ∆s ,with respect to change in time ,∆t . But as we choose time intervals closer to each other ,say 11.00001 and 11 ,then that ∆t becomes a number very very close to zero,though not perfectly zero. So in this example,∆t is like that variable h which also is present in the denominator and tends to zero. Pls let me know if you have any questions....

@@EnjoyMath thank you mam for the explanation so it means i can take any variable.

Happy to be of help 👍 👍 definitely,we can take any variable instead of h....it's just that in some books, specific variables are used to maintain uniformity 👍👍

@@legendkaiyt s=ut+1/2at² Here, u=0, a=9.8, Therefore, s= 9.8t²/2 s= 4.9t² Pls let me know if you have any questions...

There are infinite numbers between 1 and 1.1....

@@EnjoyMath Hence it not possible to know the exact value of the number which is closest to / just next to 0. So, In differentiation when the denominator (delta x) tends to 0 and correspondingly the Numerator, its function (delta y) must also be tending to some number. That value of the (delta y) is called as the 'limiting value'. dy/dx then means : the limiting value of the function divided by (delta x) as it tends to 0. We do not know the exact values of neither the numerator nor the denominator. But still the limiting value is considered/picked/accepted because we *don't* know what number falls immediately afterwards 0. I think that students don't understand dx or the concept of variable tending to another number (eg x->0) because they fail to realise that there are inifinite numbers between *ANY* two given numbers. Also, the best way to deal with this uncertainty is to have faith in god and admit how limited our knowledge is.

@@EnjoyMath Just as we don't know whats larger than the largest (Universe). Likewise we also don't know whats tinier than the tiniest(eg.Sub atomic particle electron)

Wow...your explanation and point of view reflects the deep thinking you have done on this topic....you have just explained the very vital truth that all students should appreciate....the universe out there is beyond our limited levels of thinking....it's very humbling and liberating too... If student and teacher both interact with this truth in mind that they both are in the same boat...that both are eternal students in this school of life....then education would be so much more interesting and enjoyable... Thank you so very much for sharing your wonderful thoughts!! Really appreciate it !! 😊😊👍👍👍👍

@@EnjoyMath Thank you so much. Hare Krishna.

The answers we get from differentiation are quite accurate,not approximate,and hence useful in space calculations....pls let me know the reason why it appears to be approximate value....

@@EnjoyMath oh Thankyou for the info then we can use in space calculation wow great but will there be any micron difference in exact answer and answers we from differentiation

Most welcome!! Yes, maybe there will be micron difference...it's a good question....I am not that aware of how the scientists take care of any micron differences that may arise...I have heard that they do take in to account for the human and mathematical approximations in their calculations...but I don't know the details...if any of our viewers know about it...pls do share in the comments section 👍👍👍

@@EnjoyMath We are third party' design small components for private jet body parts I don't do manual calculation but we use software for design and measuring the distance and gaps even if there is a 0.001 difference or gap they will not accept that will lead to air leak and pressure difference ultimately lead to damages or wrost cases blow out the chamber

Wow...that's really awesome information..thanks!! I think the differentiation concept is in the software code....

Thank you so much for the moving words...it's reality that we are all part of one big universal family 😊😊😊👍👍👍

Hello, y formula is 1/2 at^2, a is 9.8, and 9.8/2= 4.9 Hence y= 4.9t^2 Pls let me know if you have any questions

​@@EnjoyMath oh I thought 2 as 20 mam cuz there's written "stone reaches the ground in 20s" and 9.8/20 = 0.49 so yeah, ty mam

Most welcome 👍👍👍

Sure, I will try my best to make the videos....no problem...daily and correct practice is all that is needed to become strong in math 👍👍👍

1/2* 9.8= 4.9 where 9.8 is acceleration due to gravity,pls let me know if you have any questions...

Sure, kaunse chapters ?

Hello, we are using 9.8 as acceleration due to gravity, however the formula is 0.5 x acceleration x t², so 0.5x 9.8 = 4.9....i have not shown this calculation in the video.... Pls let me know if you have any questions....

Y we have to take the 0.5 ×g for what purpose if we need take gravity means 9.8 is enough bu y we using this

@@MohanKumar-ym1hx the formula is s= ut+1/2 at², u=0 So a= 1/2at², 1/2= 0.5, here a is the gravity g

Differentiation tab kaam aata hai jab Hume very small change of time mein,velocity ko calculate karna hai ....∆s/∆t when ∆t is tending to zero....normal velocity toh easily find kar sakte hai... instantaneous velocity ke liye differentiation bahut useful hai.....iss video mein bataya hai ki differentiation ka matlab kya hai...dy/dx means it is rate of change of a variable y for very small change in x.... Pls let me know if you have any questions..

We have used the formula in physics - s= ut+(at²/2),here u=0,a=9.8 So on substituting above values we get s or y= 4.9t²... Pls let me know if you have any questions

V interesting to read your witty comment!! 👍👍 Does your line of work use differentiation or calculus?

@@EnjoyMath no i was just curious 😄

That's excellent!! Great going !! 👍👍👍😄

Hello,sorry ,I am not that fluent in telugu...can u reply again in another language

@@EnjoyMath i want this same topic in telugu

Oh, really Sorry, I don't know Telugu that well 🙏🙏🙏

@@Everythingofphysics sorry to know about that...

@@EnjoyMath actually I am in class 8 but I wanna know it But it feels too complicated

Really good to know about your interest in learning! Differentiation is essentially finding the change in a quantity 'y' for a very very small change in quantity 'x'.... My suggestion would be that you can first learn about functions, then limits and continuity,and then come to differentiation...then it will be easier to understand terms like limits,functions etc... All the very best in your learning!! 😊😊👍👍👍

@@shk009 sorry that it's not helped you🙏🙏🙏 which part of differentiation do you find difficult?

When you are running, the numerical variables here can be your speed, the distance travelled, the time taken for running...more speed, more distance travelled and less time taken taken...so depending on which variable is fixed, that can be made as independent variable....so for example, if we know that we are going to run for 5 km, then distance is the independent variable and speed and time will accordingly change...or else if we know that running speed is 20 km/hr, then speed is the independent variable... However , it's mostly safe to take time as independent variable because that's a quantity that is really independent of most of other quantities... Pls let me know if you have any questions...

@@EnjoyMath distance covered s is funtion of time t.so independent variable.I like your explaination!

Thank you so much!! Really happy to be of help!! 😊😊👍👍

@@EnjoyMath yes,May you remain happy.

@@EnjoyMath How can you explain rotation of earth in term of function.show numerical relation between independent and depependent variables.