Find the Derivative Of $h ( t ) = t ^ { \pi ^ { 4 } } + \left( \pi ^ { 4 } \right) ^ { t } + \pi t ^ { 4 }$

question 122

Multiple Choice

Find the derivative of $h ( t ) = t ^ { \pi ^ { 4 } } + \left( \pi ^ { 4 } \right) ^ { t } + \pi t ^ { 4 }$ .

• A) \(\pi ^ { 4 } t ^ { \left( \pi ^ { 4 } - 1 \right) } + t \left( \pi ^ { 4 } \right) ^ { t - 1 } + 4 \pi t ^ { 3 }\)
• B) \(\pi ^ { 4 } t ^ { \left( \pi ^ { 4 } - 1 \right) } + \left( \pi ^ { 4 } \right) ^ { + } \ln \left( \pi ^ { 4 } \right) + 4 \pi ^ { 3 }\)
• C) \(t ^ { \left( \pi ^ { 4 } - 1 \right) } \ln t + \left( \pi ^ { 4 } \right) ^ { t } \ln \left( \pi ^ { 4 } \right) + 4 \pi t ^ { 4 } \ln t\)
• D) \(4 t ^ { \pi ^ { 3 } } + 4 t \left( \pi ^ { 3 } \right) ^ { t - 1 } + 4 \pi t ^ { 4 } \ln t\)

---

Definitions:

Capital Balances

The amount of owners' equity or shareholders' equity in a business, reflecting the residual assets after deducting liabilities.

Share of the Profit

The portion of a company's earnings allocated to each outstanding share of common stock, illustrating the company's profitability on a per share basis.

Average Capital Balances

An average of the various amounts of capital held in an account over a specific period, often used to calculate interest or allocate profits and losses in partnerships.

Interest Allowance Method

A method used in accounting to allocate interest expense over the life of a debt at a constant rate.