Question

If $y = \left[(x+1)(2x+1)(3x+1)\cdots (nx+1)\right]^n$, then $\left.\frac{dy}{dx}\right|_{x=0}$ is

• A. $\frac{1}{\sqrt{2}}$
• B. $\frac{1}{4\sqrt{2}}$
• C. $\frac{-1}{4\sqrt{2}}$
• D. $\frac{-1}{\sqrt{2}}$

Hint:

Calculus Tip: When dealing with limits at infinity involving nested radicals, double rationalization is a common and effective technique to eliminate the indeterminate forms before factoring out the highest power of $x$.

Answer 1

The Correct Option is B