# How do find the derivative of #y= (1- sec x)/ tan x#?

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To find the derivative of (y = \frac{1 - \sec(x)}{\tan(x)}), we use the quotient rule. The quotient rule states that if (u) and (v) are differentiable functions of (x), then the derivative of (\frac{u}{v}) is (\frac{u'v - uv'}{v^2}). Applying the quotient rule to the given function, we have:

[y' = \frac{(\tan(x) \cdot \sec(x) - (1 - \sec(x)) \cdot \sec^2(x))}{\tan^2(x)}]

Simplify the expression:

[y' = \frac{\tan(x) \cdot \sec(x) - (1 - \sec(x)) \cdot \sec^2(x)}{\tan^2(x)}]

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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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