The Path of an Object Moving in Xyz-Space Is Given $( x ( t ) , y ( t ) , z ( t ) ) = \left( 3 t ^ { 2 } , t + 1 , t ^ { 3 } \right)$

question 26

Essay

The path of an object moving in xyz-space is given by $( x ( t ) , y ( t ) , z ( t ) ) = \left( 3 t ^ { 2 } , t + 1 , t ^ { 3 } \right)$ .
The temperature at a point (x, y, z)in space is given by $f ( x , y , z ) = x ^ { 2 } y - 3 z$ Calculate the directional derivative of f in the direction of $\vec { v }$ at the point (12, 3, 8), where $\vec { v }$ is the velocity vector of the object..

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