Question

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

• A. $\frac{n(n+1)}{2}$
• B. $\frac{n^{2}(n+1)}{2}$
• C. $\frac{n(n+1)}{4}$
• D. $\frac{n^{2}(n-1)}{2}$

Hint:

Calculus Tip: When differentiating the product of many terms, logarithmic differentiation is the fastest and most reliable method to turn massive product rules into simple sum rules.

Answer 1

The Correct Option is B