Consider the function f$($x$,$y$,$z$)=$e$^(5$xyz$-1),$ the point P$(0,3,-2),$ and the unit vector u$=($:$(1)/(3),-(2)/(3),(2)/(3)$:$).$

a$.$ Compute the gradient of f and evaluate it at P$.$

b$.$ Find the unit vector in the direction of maximum increase of f at P$.$

c$.$ Find the rate of change of the function in the direction of maximum increase at P$.$

d$.$ Find the directional derivative at P in the direction of the given vector.