Differentiate `x^n` by first princeple

Explanation

Let `y=x^n`

Then` (dy/dx)=f'(x)=lim_(h->0)(f(x+h)-f(x))/(h)`

=`lim_(h->0)((x+h)^n-x^n)/h`

=`lim_(h->0)((x+h)^n-x^n)/(x+h-x)`

As `h->0,x+h->x`

=`lim_(x+h->x)((x+h)^n-x^n)/(x+h-x)`

=`n.x^(n-1)`

So `(dy/dx)`=`n.x^(n-1)`