# How do you differentiate #f(x)=cot(3x) # using the chain rule?

Therefore,

Now we use the chain rule.

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To differentiate ( f(x) = \cot(3x) ) using the chain rule:

- Identify the outer function ( \cot(3x) ) and the inner function ( 3x ).
- Differentiate the outer function with respect to its inner function: ( \frac{d}{dx} \cot(u) = -\csc^2(u) \cdot \frac{du}{dx} ), where ( u = 3x ).
- Differentiate the inner function ( 3x ) with respect to ( x ): ( \frac{d}{dx}(3x) = 3 ).
- Substitute the results from steps 2 and 3 into the chain rule formula to get the final result: ( \frac{d}{dx} \cot(3x) = -3\csc^2(3x) ).

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