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, Leibniz formula can be proved.
The meaning of each symbol:
σ-sum symbol.
C (n, k)- combination symbol, that is, the combination of n and k.
N-k derivative of u (n-k)-u.
The k-th derivative of v (k)-v.
This formula is similar to binomial theorem in permutation and combination, and the number of powers in binomial theorem is changed to the number of derivatives.
(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.
Related content explanation:
Gottfried Wilhelm Leibniz, a German philosopher and mathematician, is a rare generalist in history and is known as Aristotle in17th century. He is a lawyer himself and often travels to and from big cities. Many formulas were completed in a bumpy carriage, and he called himself a baron.
Leibniz occupies an important position in the history of mathematics and philosophy. Mathematically, both he and Newton discovered calculus independently, and the mathematical symbols of calculus he used were more extensive. The symbols invented by Leibniz are generally considered to be more comprehensive and have a wider scope of application. Leibniz also invented and perfected the binary system.