# How do you differentiate #f(x)=ln2x * cot(5-x)# using the product rule?

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To differentiate the function ( f(x) = \ln(2x) \cdot \cot(5-x) ) using the product rule, follow these steps:

- Identify the two functions being multiplied: ( \ln(2x) ) and ( \cot(5-x) ).
- Apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function, plus the first function times the derivative of the second function.
- Derive each function separately.
- Use the chain rule when differentiating ( \ln(2x) ).
- Differentiate ( \cot(5-x) ).
- Combine the results to find the derivative of ( f(x) ).

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