Find the Derivative of Y with Respect to the Appropriate $y = \operatorname { csch } ^ { - 1 } \left( \frac { 1 } { 3 } \right) ^ { \theta }$

question 60

Multiple Choice

Find the derivative of y with respect to the appropriate variable.
- $y = \operatorname { csch } ^ { - 1 } \left( \frac { 1 } { 3 } \right) ^ { \theta }$

• A)\(\ln \frac { 1 } { 3 }\)
• B) \(\frac { \ln 3 } { \left( \frac { 1 } { 3 } \right) ^ { \theta } \sqrt { 1 + \left( \frac { 1 } { 3 } \right) ^ { \theta } } }\)
• C) \(\frac { \left( \frac { 1 } { 3 } \right) ^ { \theta } \ln 3 } { \sqrt { 1 + \left( \frac { 1 } { 3 } \right) ^ { 2 \theta } } }\)
• D) \(\frac { \ln 3 } { \sqrt { 1 + \left( \frac { 1 } { 3 } \right) ^ { 2 \theta } } }\)

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