Find the directional derivative offat the given point in the direction indicated by the angleθ.

f(x, y) =xsin(xy), (3, 0),θ=π/4

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- Mar 8th 2009, 01:57 PMacg716Find the directional derivative of f at the given angle
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 - Mar 8th 2009, 03:59 PMthelostchild
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} $