Find the derivative of the function $(ax + b)^n$ with respect to $x$,where $a$ and $b$ are fixed non-zero constants and $n$ is an integer.

Let $f(x) = (ax + b)^n$.
By the first principle of derivatives,$f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$.
$f'(x) = \lim_{h \to 0} \frac{(a(x+h) + b)^n - (ax + b)^n}{h}$.
$f'(x) = \lim_{h \to 0} \frac{(ax + b + ah)^n - (ax + b)^n}{h}$.
$f'(x) = \lim_{h \to 0} \frac{(ax + b)^n (1 + \frac{ah}{ax+b})^n - (ax + b)^n}{h}$.
Using the binomial expansion $(1+z)^n = 1 + nz + \frac{n(n-1)}{2}z^2 + \dots$,we get:
$f'(x) = \lim_{h \to 0} \frac{(ax + b)^n [1 + n(\frac{ah}{ax+b}) + \dots] - (ax + b)^n}{h}$.
$f'(x) = (ax + b)^n \lim_{h \to 0} \frac{n(\frac{ah}{ax+b}) + \dots}{h}$.
$f'(x) = (ax + b)^n \cdot \frac{na}{ax+b} = na(ax + b)^{n-1}$.