$\text { Find the first partial derivatives of the function } f ( x , y , z ) = 2 x ^ { 3 } + 9 x y + 3 y z - z ^ { 5 } \text {. }$

question 13

Short Answer

$\text { Find the first partial derivatives of the function } f ( x , y , z ) = 2 x ^ { 3 } + 9 x y + 3 y z - z ^ { 5 } \text {. }$

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Definitions:

Bonneville Salt Flats

A vast salt flat in Utah, USA, known for its role in land speed records due to its flat, smooth surface.

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A region in the U.S. state of Washington characterized by unique geological formations created by cataclysmic flooding during the last Ice Age.

Potholes

Circular or oval depressions found on the road surface or in river beds, caused by wear and erosion.

Ripples

Small, wave-like ridges on a surface, typically formed by the action of water or wind on sand, sediment, or other fine particles.