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\[f(x,y)= \sin(xy)\]
at \[2,\frac{\pi}{4}\]

do you mean f(x)=sinx. f(y)=siny

no, f(x,y)= sin(xy)
Find
\[d_{\theta}f(2, \frac{\pi}{4})\]

Okay, easiest way to do this is with gradients.

oh looks like composite function.

my answer is 0. is this right?

Hang on...

So, first, you need to get the unit vector of
\[<2, \frac{\pi}{4}>\]