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EXAMPLE 2Finding the Partial Derivatives of a Function at a Point (x0,y0)

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