Use Logarithmic Differentiation to Find the Derivative of Y $$y = \frac { x \sin x } { \sqrt { x + 1 } }$$

question 243

Multiple Choice

Use logarithmic differentiation to find the derivative of y.
- $$y = \frac { x \sin x } { \sqrt { x + 1 } }$$

• A) \(\frac { x \sin x } { \sqrt { x + 1 } } \left( \frac { 1 } { x } + \cot x - \frac { 1 } { 2 x + 2 } \right)\)
• B) \(\left. \frac { x \sin x } { \sqrt { x + 1 } } \ln x + \ln \sin x - \frac { 1 } { 2 } \ln ( x + 1 ) \right)\)
• C) \(\frac { 1 } { x } + \cot x - \frac { 1 } { 2 x + 2 }\)
• D) \(\frac { 1 } { 2 } \left( \frac { 1 } { x } + \frac { 1 } { \sin x } + \frac { 1 } { x + 1 } \right)\)

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A method used in manufacturing to determine the quantity of materials required for production, focusing on minimizing costs while meeting production schedules.

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