I have the problem:
"suppose that over a certain region of space the electrical potential V is given by $V(x,y,z)=5x^2+3xy+xyz$.
Find the rate of change of potential at $P(3,4,5)$ in the direction of the vector $v=i+j-K$.
I tried:
$|v|=\sqrt{3}$
$u= \frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}}\frac{(-1)}{\sqrt{3}}$
$F_x=10x+3y+yz$
$F_y=3x+xz$
$F_z=xy$
$D_uf=\frac{10x+3y+yz}{\sqrt{3}}+\frac{3x+xz}{\sqrt{3}}-\frac{xy}{\sqrt{3}}$
$D_uf=\frac{30+12+20}{\sqrt{3}}+\frac{9+15}{\sqrt{3}}-\frac{12}{\sqrt{3}}=\frac{74}{\sqrt{3}}$
But the answer is $\frac{32}{\sqrt{3}}$.