**Category : **JEE Main & Advanced

G.W. Leibnitz, a German mathematician gave a method for evaluating the \[{{n}^{th}}\] differential coefficient of the product of two functions. This method is known as Leibnitz’s theorem.

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**Statement of the theorem : **If \[u\] and \[v\] are two functions of \[x\] such that their \[{{n}^{th}}\] derivative exist then \[{{D}^{n}}(u.v.)=\]\[^{n}{{C}_{0}}({{D}^{n}}u)v{{+}^{n}}{{C}_{1}}{{D}^{n-1}}u.Dv{{+}^{n}}{{C}_{2}}{{D}^{n-2}}u.{{D}^{2}}v+...........\]\[{{+}^{n}}{{C}_{r}}{{D}^{n-r}}u.{{D}^{r}}v+.........+u.({{D}^{n}}v).\]

The success in finding the \[{{n}^{th}}\] derivative by this theorem lies in the proper selection of first and second function. Here first function should be selected whose \[{{n}^{th}}\] derivative can be found by standard formulae. Second function should be such that on successive differentiation, at some stage, it becomes zero so that we need not to write further terms.

*play_arrow*Introduction*play_arrow*Some Standard Differentiation*play_arrow*Theorems for Differentiation*play_arrow*Methods of Differentiation*play_arrow*Differentiation of a Function with Respect to Another Function*play_arrow*Successive Differentiation or Higher Order Derivatives*play_arrow*\[{{n}^{th}}\] Derivative Using Partial Fractions*play_arrow*Differentiation of Integral Function*play_arrow*Leibnitz?s Theorem*play_arrow*Definition*play_arrow*Higher Partial Derivatives*play_arrow*Euler's Theorem on Homogeneous Functions*play_arrow*Deduction of Euler?s Theorem*play_arrow*Derivative as the Rate of Change

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