- #1

- 189

- 51

suppose we have a function ##C(x, y)## into the real numbers. Suppose also that ##y=y(x)##, i.e. ##y## is a function of ##x##.

Now in my script, I have a term ##\nabla_x C(x_0, y(x_0)) ##. From my point of view, this means that you take the partial derivative of ##C(x,y)## with respect to x and then insert ##y(x_0)## for ##y##, and ##x_0## for ##x##.

I would not consider the x-derivative of ##y(x)##, since then the subscript at the nabla operator wouldn't make any sense as this would simply be ##\nabla C(x_0, y(x_0))##.

Is this line of thinking correct?

Best

SL.