what is the differentiation of n^n ???

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jeew-m | College Teacher | (Level 1) Educator Emeritus

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`y = n^n`

There are two possibilities we should consider here.

One is that n is constant(which x is independent variable) and the other n is the independant variable.

Let us say n is a constant.

`y = n^n`

`(dy)/(dx) = 0`

Let us say n is independent variable.

`y = n^n`

`lny = ln(n^n)`

`lny = nlnn`

By differentiation;

`1/yxx(dy)/(dn) = nxx1/n+lnn`

`(dy)/(dn) = y(1+lnn)`

`(dy)/(dn) = n^n(1+lnn)`


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