Simple derivative?

Question

Mathematics

In the translation of the book, which was slipped to me for proofreading, I came across the phrase

"The derivative of (y - w * x) ** 2 with respect to w is -2 * (y - w * x) * x" .

"-2" is minus two, not a hyphen.
The last time I counted derivatives about thirty-five years ago, in the tenth grade of high school: develop, kind people, my suspicions about this equation. It doesn't seem right to me, but I'm not sure of myself at all.

Answer 1

A purely amateurish analysis of the example based on school memories:
(y - w * x) ^ 2 = y ^ 2 - 2ywx + (wx) ^ 2
We look at what will happen to each term on the right side of the expression if we apply the derivative with respect to w:
y ^ 2 = will be a constant, we will immediately forget about it.
- 2yx = coefficient first order (we look at the school rules, something happens with linear functions).
2x^2 w = coefficient second order (we look at the school rules, something happens to the parabola).
We get:
- 2yx + 2x^2 w Let
's take something out of the brackets:
2x (-y + xw)
Write a beautiful minus:
-2x(y - xw)

Answer 2

The derivative with respect to w is -2*x*w

Answer 3

This is the derivative of the combination: (f(g(x)))' = f'(g(x))*g(x).
In your case f(z) = z^2, g(w)=yw*x.
f(g(w)) = f(yw*x) = (y - w*x)^2
f'(z) = 2z, g'(w) = -x
Substitute in the first formula:
2(y - w *x)*(-x) - exactly what is written in the book.