Suppose That $z = x - y , x = 4 \left( t ^ { 3 } - 1 \right)$

question 57

Essay

Suppose that $z = x - y , x = 4 \left( t ^ { 3 } - 1 \right)$ , and $y = \ln t$ . Find $\frac { d z } { d t }$ .

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Definitions:

Actual Authority

The specific power given to an agent by a principal, derived from their agreement and can be express or implied based on their actions.

Apparent Authority

The perception by a third party that an agent has the authority to act on behalf of a principal, even if such authority has not been explicitly or implicitly granted.

Principal Liable

Refers to the legal responsibility of the principal party in a relationship (such as an employer) for certain actions of their agents or employees under the doctrine of vicarious liability.

Apparent Authority

The impression given to third parties that an agent is authorized to act on behalf of a principal, even if such authority has not been formally granted.