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?!” :sunglasses:

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 yx1 + 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 :sweat_smile:

It was my pleasure, glad I was able to help you out.