Compute the gradient vector fields of the following functions:

A. $f(x, y) = 3 x^2 + 6 y^2$
$\nabla f(x, y) =$ $\bf i +$ $\bf j$

B. $f(x, y) = x^{2} y^{8},$
$\nabla f(x, y) =$ $\bf i +$ $\bf j$

C. $f(x, y) = 3 x + 6 y$
$\nabla f(x, y) =$ $\bf i +$ $\bf j$

D. $f(x, y, z) = 3 x + 6 y + 2 z$
$\nabla f(x, y) =$ $\bf i +$ $\bf j +$ $\bf k$

E. $f(x, y, z) = 3 x^2 + 6 y^2 + 2 z^2$
$\nabla f(x, y, z) =$ $\bf i +$ $\bf j +$ $\bf k$