# How do you differentiate #tan x + sec y - y = 0#?

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To differentiate ( \tan(x) + \sec(y) - y = 0 ) with respect to ( x ), use implicit differentiation:

[ \frac{d}{dx}(\tan(x)) + \frac{d}{dx}(\sec(y)) - \frac{d}{dx}(y) = 0 ]

Differentiate each term individually:

[ \sec^2(x) + \sec(y)\tan(y) - \frac{dy}{dx} = 0 ]

To isolate ( \frac{dy}{dx} ), rearrange the equation:

[ \frac{dy}{dx} = \sec^2(x) + \sec(y)\tan(y) ]

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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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