Answer
$\lt 2xe^{yz^2}, x^2z^2e^{yz^2}, 2x^2yze^{yz^2}\gt $
Work Step by Step
Given: $f(x,y,z)=x^2e^{yz^2}$
$f_x=2xe^{yz^2}$
$f_y=x^2z^2e^{yz^2}$
$f_z=2x^2yze^{yz^2}$
Gradient vector of $f$ is:
$\lt 2xe^{yz^2}, x^2z^2e^{yz^2}, 2x^2yze^{yz^2}\gt $