# How do you implicitly differentiate #-3=cos(y-x)/x#?

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To implicitly differentiate (-3 = \frac{\cos(y-x)}{x}):

Differentiate both sides of the equation with respect to (x), using the quotient rule on the right side.

The derivative of (-3) with respect to (x) is (0).

For the right side, apply the quotient rule:

Let ( u = \cos(y-x) ) and ( v = x ).

Then, ( u' = -\sin(y-x)(y'-x') ) and ( v' = 1 ).

Using the quotient rule, the derivative of (\frac{u}{v}) is:

[ \frac{d}{dx}\left(\frac{u}{v}\right) = \frac{u'v - uv'}{v^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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