Find the Directional Derivative Of $f ( x , y , z ) = 3 x y z ^ { 2 } - 4 x z$

question 39

Essay

Find the directional derivative of $f ( x , y , z ) = 3 x y z ^ { 2 } - 4 x z$ at the point (3, 3, 2), in the direction of the vector $\vec { v } = 2 \vec { i } + 3 \vec { j } - \vec { k }$

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Definitions:

Evaluate

To calculate the value of an expression or assess the significance of something in a given context.

Fraction

A mathematical expression representing a part of a whole, typically written with a numerator and a denominator.

Exponentiation

A mathematical action that consists of elevating a number to the exponent of another number.

Addition

Addition is the mathematical process of combining two or more quantities to find their total or sum.