# How do you differentiate # f(x) = tan^2(3/x) #?

This could be rephrased as

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To differentiate ( f(x) = \tan^2\left(\frac{3}{x}\right) ), you would use the chain rule. The derivative of (\tan(u)) with respect to (u) is ( \sec^2(u) ), and the derivative of ( \frac{3}{x} ) with respect to (x) is ( -\frac{3}{x^2} ). Applying the chain rule, we get:

[ \frac{d}{dx}\left[\tan^2\left(\frac{3}{x}\right)\right] = 2\tan\left(\frac{3}{x}\right)\sec^2\left(\frac{3}{x}\right)\left(-\frac{3}{x^2}\right) ]

Simplifying further:

[ = -\frac{6\tan\left(\frac{3}{x}\right)}{x^2}\sec^2\left(\frac{3}{x}\right) ]

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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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