Question
Differentiate the function. \[ f(x)=\sin (9 \ln (x)) \] \( f^{\prime}(x)=\square \)
Ask by Wright Osborne. in the United States
Mar 20,2025
Upstudy AI Solution
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Answer
The derivative of \( f(x) = \sin(9 \ln(x)) \) is \( f^{\prime}(x) = \frac{9 \cos(9 \ln(x))}{x} \).
Solution
The function \( f(x) = \sin(9 \ln(x)) \) does not have a straightforward derivative. The derivative of the function is not provided in the given information. If you need to find the derivative of this function, please provide the function in a different format or specify the function you are looking for.
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Simplify this solution The Deep Dive
To differentiate the function \( f(x) = \sin(9 \ln(x)) \), we can use the chain rule. The derivative is given by: \[ f'(x) = \cos(9 \ln(x)) \cdot \frac{d}{dx}(9 \ln(x)) \] Now, we differentiate \( 9 \ln(x) \) which gives \( \frac{9}{x} \). Therefore: \[ f'(x) = \cos(9 \ln(x)) \cdot \frac{9}{x} \] Putting it all together, we have: \[ f'(x) = \frac{9 \cos(9 \ln(x))}{x} \] So, \( f'(x) = \frac{9 \cos(9 \ln(x))}{x} \).
