Anyikwa’s Derivative Formulae was developed in light to cut short the rigorous steps a mathematician has to take when he is to calculate a distant derivative.
For Instance, advances in mathematics may require that one calculates the 6th, 7th, 8th, 9th up to the 20th derivative of a function. Yes, this can be calculated but why waste so much time and the risks of making mistakes when one could easily employ ADF.
Example:y=x^11. Calculate the 9th derivative.
Normal calculation: dy/dx=〖Anx〗^(n-1) (Using that)
(d^2 y)/〖dx〗^2 =〖110x〗^9.
(d^3 y)/〖dx〗^3 =〖990x〗^8.
(d^4 y)/〖dx〗^4 =〖7920x〗^7.
(d^5 y)/〖dx〗^5 =〖55440x〗^6.
(d^6 y)/(dx^6 )=〖332640x〗^5.
(d^7 y)/〖dx〗^7 =1663200x^4.
(d^8 y)/〖dx〗^8 =6652800x^3.
(d^9 y)/〖dx〗^9 =19958400x^2.

Using ADF:
If y=x^n
(d^n y)/〖dx〗^n =〖(±)〗^N An!/(n-N)! x^(n-N)
(d^9 y)/〖dx〗^9 =(1×11!)/(11-9)! x^(11-9).
(d^9 y)/〖dx〗^9 =〖39916800x〗^2/2.
(d^9 y)/〖dx〗^9 =〖19958400x〗^2.
Explanation of the calculation using ADF.
Using ADF:
If y=x^n
(d^n y)/〖dx〗^n =〖(±)〗^N An!/(n-N)! x^(n-N)
A; The constant term of the original function.
n; The original power of the function.
n!; The factorial value of the original power.
N; The derivative one is required to find.
〖(±)〗^N; The operation for ascertaining the sign of the final derivative.
In computing An!, one has to find the factorial value of the power separately before multiplying to the constant term A.
i.e. n!×A
ADF implores the understandable principles of permutation to eliminate the clumsiness of the rigorous risk taking step by step calculation.
ADF just makes it better.
Proudly, #ThoughtandSociety.
Anyikwa Chukwuemeka.


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