# How do you find the derivative of #y=tan(2x)# ?

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To find the derivative of ( y = \tan(2x) ), use the chain rule.

[ \frac{d}{dx}[\tan(u)] = \frac{d}{du}[\tan(u)] \cdot \frac{du}{dx} ]

Here, ( u = 2x ), so ( \frac{du}{dx} = 2 ).

Now, the derivative of ( \tan(u) ) with respect to ( u ) is ( \sec^2(u) ).

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

Therefore, the derivative of ( y = \tan(2x) ) is ( \frac{dy}{dx} = 2\sec^2(2x) ).

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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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