What is the slope of the line tangent to the curve 3y2 - 2x2 = 6 - 2xy at the point (3,2)?

 The slope of the tangent line at the point (3, 2) is

Step-by-step explanation:  We are given to find the slope of the line tangent to the following curve at the point (3, 2).

We know that the derivative of a function at any given point is equal to the slope of the tangent at that point.

Now, differentiating both sides of equation (i) with respect to x, we have

So, at the point (3, 2), we get

Thus, the slope of the tangent line at the point (3, 2) is

The slope of the tangent at point (3,2) will be () and it can be evaluated by differentiating the given equation of curve.

Given :

To determine the slope of the tangent, differentiation of the given equation of curve is carried out.

Differentiating equation (1) with respect to x.

Now, further simplification of the above equation gives:

Now, at point (3,2) the slope of the tangent will be:

So, the slope of the tangent at point (3,2) will be ().

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