MHB Determine an expression using binomial theorem

[Ernie1]

Determine an expression for f(x) =(1+x)(1+2x)(1+3x)…(1 +nx),find f⸍(0) .

 

[Opalg]

Determine an expression for f(x) =(1+x)(1+2x)(1+3x)…(1 +nx),find f⸍(0) .

Hi Ernie, and welcome to MHB!

Here's a hint that may help you. If you have a polynomial $f(x) = a_nx^n + a_{n-1}x^{n-1} + \ldots + a_1x + a_0$, then $f'(0) = a_1$. In other words, to find $f'(0)$ you only need to find the coefficient of $x$ in $f(x)$.