$$\text { Find the derivative } \frac { d } { d t } \left[ \mathbf { r } ( 4 t ) \cdot \mathbf { r } \left( t ^ { 4 } \right) \right]$$

question 152

Short Answer

$$\text { Find the derivative } \frac { d } { d t } \left[ \mathbf { r } ( 4 t ) \cdot \mathbf { r } \left( t ^ { 4 } \right) \right]$$

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Definitions:

Volume

The amount of space that an object or substance occupies or contains, measured in cubic units.

Material

The substance or substances out of which a thing is or can be made, often categorized by its physical properties, such as hardness, elasticity, and density.

Liquid Sample

A portion or quantity of liquid taken to represent the whole, used for analysis or testing.

Density

The mass of a substance per unit volume, often expressed in grams per cubic centimeter or kilograms per cubic meter.