(d) f(x,y,z)=xye^z+yze^x,P=(1,0,0) , véc tơ từ P đến (2,2,1)

The question is asking for the gradient of the function $f(x,y,z)=xye^{z}+yze^{x}$ at the point $P=(1,0,0)$, and then to find the vector from $P$ to $(2,2,1)$. The gradient of a function gives us a vector that points in the direction of the steepest ascent of the function. It is found by taking the partial derivative of the function with respect to each variable. The vector from $P$ to $(2,2,1)$ is simply the difference between the coordinates of $(2,2,1)$ and $P$.