Differentiate x(x+1)(x+2).

Differentiate x(x+1)(x+2).

first foil (x+1)(x+2)= x(x^2+3x+2)
then distribute the x: (x^3+3x^2+2x)
then take the derivative: 3x^2 +6x+2

Use the product rule.

x'(x+1)(x+2) + x(x+1)'(x+2) + x(x+1)(x+2)'
The derivative of x' is 1. The derivatives of x+1 and x+2 are also 1.
= (x+1)(x+2) + x(x+2) + x(x+1)

This question was answered by a Teen Tech Tutor volunteer at the Olympia Timberland Library.

by product rule,
derivate of fgh = f'gh + fg'h + fgh'

so derive of x(x+1)(x+2) is
1(x+1)(x+2) + x(1)(x+2) + x(x+1)(1)
=x^2+3x+2 + x^2+2x + x^2+x
=3x^2+6x+2