Question

How do you differentiate `f(x)=(x+1)(x+2)(x+3)` using the product rule?

Answer 1

You consider two of the factors as one, doing somewhat of a chain rule here.

Explanation:

In general terms, we can state that a product rule for three terms can be depicted as follows:

`(abc)'=(ab)'c+(ab)c'=(a'b+ab')c+(ab)c'=color(green)(a'bc+ab'c+abc')`

Let's do it for your `f(x)=(x+1)(x+2)(x+3)`:

`(df(x))/(dx)=(1)(x+2)(x+3)+(x+1)(1)(x+3)+(x+1)(x+2)(1)`

`(df(x))/(dx)=color(green)(3x^2+12x+11)`