Compute the partial derivatives with respect to x :
[tex]f(x,y)=g(y)+\tan^{-1}(xy)[/tex]
[tex]\implies f_x(x,y)=\dfrac y{1+(xy)^2}[/tex]
[tex]\implies f_{xx}(x,y)=-\dfrac{2xy^3}{(1+(xy)^2)^2}[/tex]
Evaluate the second partial derivative at (2, 1) :
[tex]\implies f_{xx}(x,y)=\boxed{-\dfrac4{25}}[/tex]
