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# Leibniz Rule (Differentiation)

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Consider . Show that - I can do that.

By differentiating this equation n times using Leibniz's rule, show that .

I literally have no idea where to start =\ .
2. (Original post by ViralRiver)

Consider . Show that - I can do that.

By differentiating this equation n times using Leibniz's rule, show that .

I literally have no idea where to start =\ .
Without sounding harsh, have you actually tried to plug it into the General Leibniz rule?
(namely with and
3. (Original post by Farhan.Hanif93)
Without sounding harsh, have you actually tried to plug it into the General Leibniz rule?
(namely with and
That's not how I learned it. The version I have learned is:

.

I've tried substituting into that, but it's a tad confusing.
4. (Original post by ViralRiver)
That's not how I learned it. The version I have learned is:

.

I've tried substituting into that, but it's a tad confusing.
I've never come across that notation before but I assume that ? In which case, you should be able to see that both versions are equivalent. In your notation, take and . Notice that all terms have a factor of . What happens to that quantity when (if it's not immediate, try a few values.)
5. (Original post by Farhan.Hanif93)
I've never come across that notation before but I assume that ? In which case, you should be able to see that both versions are equivalent. In your notation, take and . Notice that all terms have a factor of . What happens to that quantity when (if it's not immediate, try a few values.)
I'll take another look at it tomorrow - don't think I can work this late :P . However, I don't see any form of binomials in your expression?
6. (Original post by ViralRiver)
I'll take another look at it tomorrow - don't think I can work this late :P . However, I don't see any form of binomials in your expression?
You're right, it is late! I even forgot to put in the coefficients... Sorry for any confusion on that front.

7. evaluate first two terms in the sum ie k = 0 and 1.

get the binomial coefficients and differentiate the second x term once

the rest of the sum is zero as all remaining derivatives of x order 2 or higher are zero (differentiation with respect to x)
giving
8. Thanks a lot for your help guys - makes a lot more sense now.
9. (Original post by swelshie)

evaluate first two terms in the sum ie k = 0 and 1.

get the binomial coefficients and differentiate the second x term once

the rest of the sum is zero as all remaining derivatives of x order 2 or higher are zero (differentiation with respect to x)
giving

(Original post by Farhan.Hanif93)
You're right, it is late! I even forgot to put in the coefficients... Sorry for any confusion on that front.
Ok it now asks me to evaluate . My guess: but not really sure what to do from there (the answer should be 0).

EDIT: I've put into the Leibniz thing and got it equal to 2y' which is of course 0, hence - is that the right method?
10. (Original post by ViralRiver)
Ok it now asks me to evaluate . My guess: but not really sure what to do from there (the answer should be 0).

EDIT: I've put into the Leibniz thing and got it equal to 2y' which is of course 0, hence - is that the right method?
Yep, that's fine.

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