# How do you find the derivative of #tan(1/x)#?

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To find the derivative of ( \tan(1/x) ), you can use the chain rule.

Let ( u = 1/x ). Then ( \tan(1/x) = \tan(u) ).

Now, differentiate ( \tan(u) ) with respect to ( u ) using the chain rule, and then multiply by the derivative of ( u ) with respect to ( x ), which is ( -1/x^2 ).

The derivative is:

[ \frac{d}{dx} \tan(1/x) = \frac{d}{du} \tan(u) \cdot \frac{du}{dx} = \sec^2(u) \cdot \left( -\frac{1}{x^2} \right) = -\frac{\sec^2(1/x)}{x^2} ]

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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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