For f(x,y)=xsiny+ysinx, find fx(π3,π6) and fy(π3,π6).
Solution We use the results from Example 1(b): fx(x,y)=siny+ycosxfx(π3,π6)=sinπ6+π6cosπ3=12+π6(12)=6+π12fy(x,y)=xcosy+sinxfy(π3,π6)=π3cosπ6+sinπ3=π3(√32)+√32=(π+3)√36