Use Logarithmic Differentiation to Find the Derivative of Y with Respect

question 429

Multiple Choice

Use logarithmic differentiation to find the derivative of y with respect to the independent variable.
- $$y = ( x + 3 ) ^ { x }$$

• A) \(x + ( 3 ) ^ { x - 1 }\)
• B) \(\ln ( x + 3 ) + \frac { x } { x + 3 }\)
• C) \(( x + 3 ) ^ { x } \left( \ln ( x + 3 ) + \frac { x } { x + 3 } \right)\)
• D) \(x \ln ( x + 3 )\)

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Definitions:

Chemical Reaction

A chemical reaction is a process that leads to the transformation of one set of chemical substances to another through the breaking and forming of chemical bonds.

Evaporative Cooling

A natural or artificial process where the evaporation of a liquid into a gas absorbs heat, reducing the temperature of the surrounding environment.

Specific Heat

The amount of heat per unit mass required to raise the temperature of a substance by one degree Celsius.

Hydrophilic

Interacting readily with water; having a greater affinity for water molecules than they have for each other. Compare with hydrophobic.