# How do you differentiate #f(x)=tan(3x)#?

Using chain rule, first differentiate tan3x w.r.t 3x and then differentiate 3x w.rt x

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The answer is

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To differentiate ( f(x) = \tan(3x) ), you can use the chain rule. The derivative of ( \tan(u) ) with respect to ( u ) is ( \sec^2(u) ), and then you multiply by the derivative of the inner function ( u ) with respect to ( x ). So, the derivative of ( f(x) ) is:

[ f'(x) = \frac{d}{dx}(\tan(3x)) = \sec^2(3x) \cdot \frac{d}{dx}(3x) = 3\sec^2(3x) ]

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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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