Q. $n$th derivative of $(x + 1)^{n}$ is equal to
A) $(n - 1)!$
B) $(n + 1)!$
C) $n!$
D) $n\left\lbrack (n + 1) \right\rbrack^{n - 1}$
Explanation
(c)
Let $y = (x + 1)^{n}$
$\therefore\ \frac{dy}{dx} = n(x + 1)^{n - 1}$
$\ \frac{d^{2}y}{dx^{2}} = n(n - 1)(x + 1)^{n - 2}$
Similarly, $\frac{d^{2}y}{dx^{n}} = n(n - 1)(n - 2)\ldots 3.2.1 = n!$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.