Let n be the number of differentiation and b be the exponent of the given term of a polynomial
- If , then the nth derivative of a given polynomial is 0.
Ex. Find the 5th derivative of ?
Since the given n is 5 and b is 4, it adheres that , so use the statement 2, thus:
To prove that this statement is correct, let's use the repeated differentiation method.
Note: If we find the 6th, 7th or either the 1000th derivative of , it will give also a derivative of 0 since n is greater than b.