# Strange Notation: $f(x,y) = \ln (x + \text {s} \space \overline {x^2 + y^2}$)

I am currently working on my first calculus assignment of the quarter, and immediately ran into a strange notation which neither my teacher discussed nor is it mentioned in any previous parts of the chapter.

$f(x,y) = \ln (x + \text {s} \space \overline {x^2 + y^2}$)

I am supposed to find a partial derivative of this function, but I have no idea what the s-overbar notation means. Google searches for "s followed by overbar expression," "math overbar," etc. turn up no useful results.

The book I am using is Calculus 6th Edition, by James Stewart. As far as I can tell, the notation first shows up in Chapter 15.3 in the practice exercises.

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Perhaps they mean the complex conjugate of $x^2 + y^2$, but then the $s$ wouldn't be there. @Sigur is probably correct. –  George V. Williams Jan 12 '13 at 18:25
I guess that it is a typo. I believe that the correct is $\sqrt{x^2+y^2}$. Since this book is not typed in TeX, I would not be surprise with this kind of typo. –  Sigur Jan 12 '13 at 18:25
Do they say wthat the domain is? Maybe that will shed some light. –  Git Gud Jan 12 '13 at 18:27
The specific problem says to find $f_x (3, 4)$. The answer given in the back of the book is $\frac {1}{5}$. –  Ryan Jan 12 '13 at 18:29
@Sigur you should write as an offical answer so the OP can accept it. –  Git Gud Jan 12 '13 at 18:33

Assuming your answer is $\frac{1}{5}$, lets see.
$$f_x(x,y)=\frac{1}{x+\sqrt{x^2+y^2}}\left(1+\frac{2x}{2\sqrt{x^2+y^2}}\right)$$ and evaluating at $(3,4)$ we will obtain $f_x(3,4)=\frac{1}{5}$.
I believe that this is the case, so $f(x,y)=\ln(x+\sqrt{x^2+y^2})$.