# Do not understand the differentiation of a Single Parameter

Hello guys,

So this concept has been bugging me for two days but I can’t get my head around it.
Apologies if this might sound like a stupid question.

In the course, they say that since an iteration of x1 and y are treated as constants, it leaves an iteration x1 in the equation.

However, what I was thinking was that since they are constants both of them should be removed when calculating the derivative.

I don’t understand how it leaves x1

Please, no worries…this is exactly what the community is for! In my opinion, the only stupid question that exists is “why don’t I feel comfortable asking this question?!”

Firstly, I haven’t done this mission yet and so I do not have much in the way of context but I do have a degree in mathematics and therefore feel quite comfortable with calculus so hopefully I can be of some use.

I’m not sure but I think this might be confusing because normally our variables are `x` and `y` while `a` is usually used for constants. However, for this scenario, `x(i)` and `y(i)` are being treated as constants and since we are differentiating with respect `a1`, it is essentially acting as our variable.

For example, the derivative of ax - b with respect to x (where a and b are constants and x is our variable) is simply a because the derivative of the sum is the sum of the derivative (ie to find the derivative of ax - b, we simply add the derivative of ax (using the power rule → a) to the derivative of -b (the derivative of a constant is 0). So the derivative of ax - b is a + 0 = a.

This is very similar to the problem in question except that our “constants” and “variable” are switched. Therefore, the derivative of `a1x1 - y` with respect to `a1` is the derivative of `a1x1` plus the derivative of `y``x1` + `0` = `x1`.

Does that help you at all? Let me know if it doesn’t and we can try something else.

Thank you very much for your explanation, Mike! I understand it now.
Math subjects always seem so logical once you get it. However, it never was my strong suit in high school