# How do you differentiate #f(x)=ln2x * cot5x# using the product rule?

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

- Identify the functions: ( u(x) = \ln(2x) ) and ( v(x) = \cot(5x) ).
- Differentiate each function: ( u'(x) = \frac{1}{x} ) and ( v'(x) = -5\csc^2(5x) ).
- Apply the product rule: ( f'(x) = u'(x)v(x) + u(x)v'(x) ).
- Substitute the derivatives and original functions into the formula.
- Simplify the expression if necessary.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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