Leibniz's law, also known as the product law, is a law for calculating the product derivative of two functions in mathematics.

Generally, if both the function u=u(x) and the function v=v(x) have n-order derivatives at point x, then:

Newton-Leibniz formula is an important formula in calculus, which links indefinite integral with definite integral and gives a perfect and satisfactory operation method of definite integral.

Extended data derivation process:

If there are functions u=u(x) and v=v(x), and both of them have n-order derivatives at x point, then obviously,

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 ' ' '

…………

Finally, it can be scientifically concluded that:

Baidu Encyclopedia-Leibniz Formula