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

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

Tardigrade Admin · Accepted Answer

Let y=(a x+ b)n Differentiating y w.r.t. x, we get (d y/d x)=n(a x+ b)n-1 (d/d x)(a x +b) =n(a x+b)n-1 a ⇒ (d y/d x)=n a(a x +b)n-1

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

$n (a x + b)^{n - 1}$

$na (a x + b)^{n - 1}$

$nb (a x + b)^{n - 1}$

$nab (a x + b)^{n - 1}$

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

Q. If a and b are fixed non-zero constants, then the derivative of (ax+b)n is

n(ax+b)n−1

na(ax+b)n−1

nb(ax+b)n−1

nab(ax+b)n−1