Find the Derivative Of $f ( t ) = \sqrt { t ^ { 5 } } + \sqrt [ 5 ] { t ^ { 2 } }$

question 4

Multiple Choice

Find the derivative of $f ( t ) = \sqrt { t ^ { 5 } } + \sqrt [ 5 ] { t ^ { 2 } }$ .

• A) \(5 t ^ { - 1 / 2 } + 2 t ^ { - 3 / 2 }\)
• B) \(\frac { 5 } { 2 } t ^ { 1 / 2 } - \frac { 2 } { 5 } t ^ { 3 / 5 }\)
• C) \(\frac { 5 } { 2 } t ^ { 3 / 2 } + \frac { 2 } { 5 } t ^ { - 3 / 5 }\)
• D) \(\frac { 2 } { 5 } t ^ { 3 / 2 } + \frac { 5 } { 2 } t ^ { - 3 / 5 }\)
• E) \(5 \sqrt { t ^ { 4 } } + 2 \sqrt [ 5 ] { t }\)
• F) \(\frac { 5 } { 2 } t ^ { 4 } - \frac { 2 } { 5 } t\)
• G) \(\frac { 3 } { 2 } t ^ { 5 / 2 } - \frac { 2 } { 3 } t ^ { 3 / 2 }\)
• H)None of the above

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Definitions:

Price Variance

The difference between the actual price paid for something and its standard or expected price.

Actual Price

The real price at which a transaction occurs, distinct from list or estimated prices, reflecting the amount paid or received in a transaction.

Standard Price

A predetermined cost attributed to materials, labor, and overhead to facilitate budgeting and variance analysis.

Efficiency Standard

A benchmark for measuring the optimal use of resources in the production of goods or the delivery of services.