Find the Derivative of the Function $\frac { e ^ { - 5 x } } { 5 x e ^ { 5 x } }$

question 27

Multiple Choice

Find the derivative of the function. $\frac { e ^ { - 5 x } } { 5 x e ^ { 5 x } }$

• A) \(- \frac { 10 x - 1 } { 5 x ^ { 2 } e ^ { 10 x } }\)
• B) \(\frac { 10 x + 1 } { 5 x ^ { 2 } e ^ { 10 x } }\)
• C) \(- \frac { 10 x + 1 } { x ^ { 2 } e ^ { 10 x } }\)
• D) \(- \frac { 10 x + 1 } { 5 x ^ { 2 } e ^ { 10 x } }\)
• E) none of these

---

Definitions:

Increasing Cost

A situation where the price of goods or services rises over time, affecting consumer behavior and economic strategies.

Payroll Inserts

Documents or messages included with employee paychecks, commonly used to communicate organizational news, policies, or updates.

Isolated Areas

Regions or locations that are geographically distant from major population centers or hard to access due to limited transportation or infrastructure.

Tax Consequences

The effects that various financial actions have on the amount of tax one must pay.