Find the directional derivative of f at the given point in the direction indicated by the angle θ.
f(x, y) = x sin(xy), (3, 0), θ = π/4
If you look in any textbook you'll find a proof (or atleast a justification) for this
the directional derivative of a function is given by
$\displaystyle \nabla f \cdot \mathbf{n} $
where n is a unit vector in the direction that your taking the derivative. And grad f is evaluated at the specified point.
in this case it would be $\displaystyle \mathbf{n}=\frac{1}{\sqrt{2}} \begin{pmatrix} 1 \\ 1 \end{pmatrix} $