(A) Differentiate $e ^ { 2 x }$ By Differentiating $e ^ { x } \cdot e ^ { x }$

question 102

Essay

(a) Differentiate $e ^ { 2 x }$ by differentiating $e ^ { x } \cdot e ^ { x }$ .(b) Differentiate $e ^ { 3 x }$ by differentiating $e ^ { x } e ^ { 2 x }$ and using the result of part (a).(c) Continue as above to find $\frac { d } { d x } e ^ { 4 x } \text { and } \frac { d } { d x } e ^ { 5 x }$ using the results from above.(d) Based upon your answers to parts (a)-(c), make a conjecture about $\frac { d } { d x } e ^ { n x }$ .

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Definitions:

Favoritism

The unfair favoring of one person or group over others based on subjective preferences rather than objective merit.

Cronyism

The practice of favoring one's close friends, especially in political appointments or business, regardless of their qualifications.

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The behavior in workplaces that involves tactics of power and influence to achieve personal or organizational gain.

Pyramid-shaped Organization

An organizational structure that is characterized by a broad base of lower-level employees and a narrowing chain of command up to the top leadership.