Leibnitz's Theorem - introduction | ExamSolutions

This is the first in a series where I introduce you to Leibnitz's Theorem for finding the nth derivative of a product of two functions.

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[kaizoniumnh]

Its heartwarming to hear this voice who helped me through my a levels and not my university life

[DiegoMathemagician]

I smiled when i recognized the binomial theorem pattern because one night i discovered it by myself and it was so satisfying... Thanks for the post, i didn't know about this :)

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[Ligerthelight]

Thats how every maths should be thought
Slow and satisfying explainingnevery step
Thank you very much, i appreciate it 😊

[mutiyasani]

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[rajvirmanku]

It hit me hardd the moment u finished writing the second differential. Tysmm!!

[SM-qkjv]

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[ScienceBronzewall]

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[oulafatla]

thank you so much for sharing the video, it was quite useful and helpful

[mariammohammed]

Thank you you explained it slowly enough to understand it even my English is not very good thank you

[AgamGaurav]

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[tomctutor]

So to summarize,
D^n{y(x)} = d^n y(x)/dx^n = y(^n)(x) given y(x) = u(x).v(x) product is:
D^n{y(x)} = ∑_(r=0, r=n) C(n, r) D^r{u}.D^(n-r)(v}
where I have intimated the *D* -operator *d/dx* with D^0{u(x)} is simply u(x)
and C(n, r) the combinatorial factor = n!/r!(n-r)!
I trust this is helpful. ヅ

[TheCalcSeries]

This video is very, very helpful. Thank you :)

[imadnessbros]

Thanks. I was wondering if you'd done any videos on Hooke's law?

[iuliusconstantcornelio]

So... Binomial Expansion, but for the gradient of a tangent to a curve....Interesting. I am quite sad inside now that I am got denyed by my college to do Further Maths....

[antoniobradiano]

please translate his work into English. It was forbiddin