derivative of the following with respect to x1: x1 + x2 +x1x2 + x1 + x3 + x1x3 - (x1)^2

Question

Mostly having trouble with the x1x2 and x1x3 derivatives for some reason, so some explanation there would be helpful.

Answer 1

When you take the derivative with respect to some variable, all the other variables are treated as constants. So, imagine you're taking this derivative instead:

 

x + 2 + 2x + x + 3 + 3x - x²

 

The derivative of that function is:

 

1 + 0 + 2 + 1 + 0 + 3 - 2x = 7 - 2x

 

 

Your function works pretty much the same way. Terms like x₂ are just constants, and terms like x₁x₂ are just your variable with a constant coefficient attached. The derivative of a constant is always 0, and the derivative of a variable with a coefficient attached is just that coefficient. So your derivative is:

 

1 + 0 + x₂ + 1 + 0 + x₃ - 2x₁ = 2 + x₂ + x₃ - 2x₁

 

 

Hope this makes sense!