$\begingroup$I need to find the directional derivative of $f(x,y,z)=xy+xz+yz$ at $P(1,2,3)$ in the direction of $\overrightarrow{v}=\langle 2,1,-1 \rangle$
I think I started this incorrectly and would greatly appreciate any hints!
$$f(x,y,z)=xy+xz+yz$$
$$f_x=y+z$$
$$f_y=x+z$$
$$f_z=x+y$$
$\endgroup$1 Answer
$\begingroup$Hint :-
If $f(x,y)$ is a function and $u$ is an unit vector then the directional derivative of $f$ in the direction of $u$ is $\nabla f.u$, where $\nabla f$ is the gradient of $f$.
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