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.