Find the directional derivative of f(x, y,z)=z3−x2yf(x, y,z)=z3−x2y at the point (−5,5,2)(−5,5,2) in the direction of the vector v=⟨−3,2,−4⟩v=⟨−3,2,−4⟩.

We are given

Firstly, we can find gradient

so, we will find partial derivatives

now, we can plug point (-5,5,2)

so, gradient will be

now, we are given that

it is in direction of v=⟨−3,2,−4⟩

so, we will find it's unit vector

now, we can find unit vector

now, we can find dot product to find direction of the vector

now, we can plug values

.............Answer