Question

If $a$ and $b$ are fixed non-zero constants, then the derivative of $(a x +b)^{n}$ is

• A. $n ( ax + b )^{ n -1}$
• B. $na ( ax + b )^{ n -1}$
• C. $nb ( ax + b )^{ n -1}$
• D. $nab(a x+ b)^{n-1}$

Answer 1

Answer: (B)

Let $y=(a x+ b)^{n}$
Differentiating y w.r.t. x, we get
$\frac{d y}{d x}=n(a x+ b)^{n-1} \frac{d}{d x}(a x +b)$
$=n(a x+b)^{n-1} a$
$\Rightarrow \frac{d y}{d x}=n a(a x +b)^{n-1}$