Leibnitz Theorem - Derivation, Solved Examples, and FAQs

In Mathematics, the Leibnitz theorem or Leibniz integral rule for derivation comes under the integral sign. It is named after the famous scientist Gottfried Leibniz. Thus, the theorem is basically designed for the derivative of the antiderivative. Basically, the Leibnitz theorem is used to generalise the product rule of differentiation. It states that if there are two functions let them be a(x) and b(x) and if they both are differentiable individually, then their product a(x). b(x) is also n times differentiable.This theorem basically refers to the process through which one can find the derivative of an antiderivative. It is also known as successive differentiation. According to the proposition, the derivative on the nth order of the product of two functions can be expressed with the help of a formula. The formula for the above-mentioned theorem is as follows:\[ (uv)^{n} = \sum_{i=0}^{n} \left(\begin{array}{c}n\\ i\end{array}\right) u^{n-i} v^{i} \]In the above expression, \[ \left(\be...