question 42

Short Answer

$$\text { Use the definition of partial derivatives as limits to find } f _ { x } ( x , y ) \text { if } f ( x , y ) = 4 x ^ { 2 } - 8 x y + 2 y ^ { 2 } \text {. }$$

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Definitions:

Sulfide Mineral

A mineral compound characterized by the presence of sulfur in combination with metals such as iron, copper, or zinc.

Cube-Shaped Crystals

Crystalline structures that manifest in a cubic shape, common in minerals like pyrite and halite.

Pink-Colored Mineral

Minerals that exhibit a pink hue, often due to the presence of elements like manganese or inclusion of minerals like rhodonite.

Wavy Lines

This term is not typically associated with a standard definition in scientific contexts; it could refer to visual patterns or features that resemble waves.