Extreme question for the brilliant - how to differentiate a combination function of nCr?

Question

Given a function of f(n) = nCr, where r is a constant,
example like, r=3, then f(6) = 6C3

How to get the differentiate of the function, ie f'(n)?

I think because nCr = n!/[(n-r)!r!],
and n! is differentiable by using gamma function, differentiate nCr is possible. But I can't even confirm whether I do it right on differentiate on n!, I got stuck on differentiate nCr.

Anybody could help me on this?

Answer 1

Look up the Beta function.
B(x,y)=
Gamma(x)Gamma(y)/Gamma(x+y).
This is essentially the reciprocal of the combination function (x=n-r, y=r).

If you just want to use the Gamma function, just do the quotient rule.

Answer 2

nCr is not differentiable because the function is not continuous, also it is only defined for integral numbers so you cant take left and right limits. If you want to extend n! so that it is continous you can use Gamma , but why the Gamma ?
You can extend n! in hundreds of ways to be continuous and differentiable

Answer 3

For awhile whilst i replaced right into a baby I ate peanut butter and miracle whip sandwiches. Or i could only arise interior the midst of the evening and devour the miracle whip precise out of the jar. My mom could devour peanut butter and bologna sandwiches. whilst human beings hear that they think of i'm gross

Answer 4

Actually I am actually not clear what you are trying to achieve by differentiaing nCr.... we used to call it from N choose R and it is a number.

Answer 5

is answer
here r is a constant
so 1/r!(diff(n!)/(n-r)!)
since n! is (n-1)1(n-2)!---------------
so diff(m/n)or apply u/v rule
and diff of n!=apply binomial expansion and solve for u/v rule
and same for (n-r)!
apply binoomial expanasion

Answer 6

gimb1960 is correct