# How do you implicitly differentiate #-1=xy-tan(x-y) #?

#frac{dy}{dx} = frac{sec^2(x-y) - y}{sec^2(x-y) + x}#

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To implicitly differentiate the equation -1 = xy - tan(x - y) with respect to x, apply the chain rule and product rule as follows:

d/dx(-1) = d/dx(xy) - d/dx(tan(x - y))

0 = y + x(dy/dx) - sec^2(x - y)(1 - dy/dx)

Rearranging the equation, we get:

dy/dx = (y - sec^2(x - y))/(x + sec^2(x - y))

This is the implicit derivative of y with respect to 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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