Since the original text is copyrighted, I cannot reprint the exact problem. But based on common patterns in Fusco-Marcellini-Sbordone, in Chapter 2 (several variables) often reads similar to:
: Detailed problems on pointwise and uniform convergence, power series, and Taylor series. Since the original text is copyrighted, I cannot
: Some professors provide specific exercise sets based on this text, such as those available through the University of Naples or University of Pisa . Since the original text is copyrighted
We evaluate this at the point $x=0$ (knowing $y(0)=0$): $$ y'(0) = - \frac-\sin(y(0))1 - 0 \cdot \cos(y(0)) $$ $$ y'(0) = - \frac-\sin(0)1 - 0 $$ $$ y'(0) = - \frac01 = 0 $$ and optimization (maxima and minima).
: Functions of two or more variables, partial derivatives, gradients, and optimization (maxima and minima).