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What is the cnk formula?
Cnk formula is Leibniz formula, and the solution is:

Leibniz formula, like binomial theorem, is used to find the higher derivative of f(x)*g(x).

(ultraviolet)' = u' v+ ultraviolet'.

(uv)'' = u''v+2u'v'+uv ' ' .

According to mathematical induction, ...

(uv) first derivative =u first derivative times v+u times v first derivative.

(uv) Second derivative =u second derivative times v+2 times U first derivative times V first derivative +u times V second derivative.

(uv) third derivative =u third derivative times v+3 times u second derivative times v first derivative +3 times u first derivative times v second derivative +u times v third derivative.

If there are functions u=u(x) and v=v(x), and both of them have n-order derivatives at point X, then it is obvious.

U (x) v (x) also has an nth derivative at x, (u v) (n) = u (n) v (n).

As for the n-order derivative of u(x) × v(x), it is more complicated. According to the basic deduction rules and formulas, we can get:

(ultraviolet)' = u'v+ultraviolet'.

(uv)'' = u''v + 2u'v' + uv ' ' .

(uv)''' = u'''v + 3u''v' + 3u'v'' + uv ' ' .