Chapter 13 - Section 13.3 - Partial Derivatives - Exercises - Page 703: 61

(a) $3$ and (b) $2$

(a) The slope of the line tangent to a surface $f(x,y)$ at the point $(a,b)$ and lying in the plane $x=a$ is given as $f_y(a,b)$. Thus, $f_y(x,y)=3 \implies f_y(-2,1)=3$ (b) The slope of the line tangent to a surface $f(x,y)$ at the point $(a,b)$ and lying in the plane $y=b$ is given as $f_x(ab)$. Thus, $f_x(x,y)=2 \implies f_x(-2,1)=2$