Question

Find the derivative of the following functions (it is to be understood that $a,b,c,d,p,q,r$ and $s$ are fixed non-zero constant and $m$ and $n$ are integers) : $(ax+b){}^n$

Answer 1

Let $f\left(x\right)=(ax+b{)}^n$
Thus using chain rule,
$f^{\prime }\left(x\right)=\frac{d(ax+b{)}^n}{d(ax+b)}\cdot \frac{d(ax+b)}{dx}$

$=n(ax+b{)}^{n-1}\cdot a$

$=na(ax+b{)}^{n-1}$