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

c. (3,2,6) is the answer.

its 50 miles away from the starting point