Need help with determining the initial rate of change of pressure a person walking a certain direction experiences The pressure in a certain region is given by $$P = x^2y - xe^z + ysin(2xz)$$.
Determine the pressure gradient at the point (1,2,0)
Determine the initial rate of change in the pressure experienced by a person setting off from this point in the direction of the vector $$2i  - 4j + k$$
I have done the first part I believe $$∇(x,y,z)$$, partially differentiating the pressure function in relation to each parameter. $$∇_x = 2xy - e^z +2yzcos(2xz)$$, $$∇_y = x^2 + sin(2xz)$$ and $$∇_z = -xze^z + 2xycos(2xz) $$ and finally substituting point (1,2,0) into each of these to get $$∇(x,y,z) = (3,1,0)$$
However, I have no idea how to do the second part of the question so any help would be appreciated.  

It is in fact the inner product of gradient vector and unit vector along the given direction i.e.$$\text{Partial variation}=\nabla f.\vec{u}=(3,1,0)\cdot(2,-4,1)\dfrac{1}{\sqrt{21}}=\dfrac{2}{\sqrt{21}}$$
