# How do you find the differential #dy# of the function #y=2x-cot^2x#?

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To find the differential (dy) of the function (y = 2x - \cot^2x), you can differentiate it with respect to (x), using the rules of differentiation. The differential is given by:

[dy = \frac{dy}{dx} , dx]

Differentiating (y) with respect to (x) gives:

[\frac{dy}{dx} = 2 - \frac{d}{dx}(\cot^2x)]

To find (\frac{d}{dx}(\cot^2x)), you can use the chain rule:

[\frac{d}{dx}(\cot^2x) = \frac{d}{dx}(1/\tan^2x) = -2\cot x \csc^2x]

Therefore,

[\frac{dy}{dx} = 2 + 2\cot x \csc^2x]

So, the differential (dy) is:

[dy = (2 + 2\cot x \csc^2x) , dx]

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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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