# What is the slope of the tangent line of #e^(xy)/(2x-y)= C #, where C is an arbitrary constant, at #(2,3)#?

I would use the fact that

The equation becomes:

Differentiating implicitly yields:

So we need only solve:

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To find the slope of the tangent line at the point (2,3) for the equation ( \frac{e^{xy}}{2x-y}= C ), we need to find the derivative of (y) with respect to (x), and then evaluate it at the point (2,3).

Differentiate both sides of the equation implicitly with respect to (x), and then solve for (y'), the derivative of (y) with respect to (x). Once you have (y'), substitute (x = 2) and (y = 3) into (y') to find the slope of the tangent line at the point (2,3).

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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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