# What is the derivative of # tan^-1 ((1.5)/x) - tan^-1 (0.5)#?

Using the Chain Rule along with the fact that

Simplify:

Getting rid of the decimals:

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The derivative of ( \tan^{-1}(\frac{1.5}{x}) - \tan^{-1}(0.5) ) is ( \frac{-1.5}{x^2(1 + (\frac{1.5}{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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