ANYIKWA’S DERIVATIVEE FORMULAE

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)
dy/dx=〖11x〗^10.
(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
Then,
(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
Then,
(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.
N.B:
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.
By,
Anyikwa Chukwuemeka.

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