Question

Directional Derivative please

Answer 1

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

Answer 2

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

Answer 3

no, f(x,y)= sin(xy)

Find
\[d_{\theta}f(2, \frac{\pi}{4})\]

Answer 4

Okay, easiest way to do this is with gradients.

Answer 5

oh looks like composite function.

Answer 6

my answer is 0. is this right?

Answer 7

Hang on...

Answer 8

Sorry, was preoccupied. The directional derivative of a function in the direction of the vector v is given by this formula:
\[\large \nabla f(x,y) \cdot \frac{v}{||v||}\]

Answer 9

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