A) Findi Consider the curve x²y + y2x = 6
dy
in terms of x and y
B) Write the equation for the tangent line where x = 2 and y = 1.

Part A)

Part B)

Step-by-step explanation:

We have the equation:

Part A)

We want to find the derivative of our function, dy/dx.

So, we will take the derivative of both sides with respect to x:

The derivative of a constant is 0. We can expand the left:

Differentiate using the product rule:

Implicitly differentiate:

Rearrange:

Isolate the dy/dx:

Hence, our derivative is:

Part B)

We want to find the equation of the tangent line at (2, 1).

So, let's find the slope of the tangent line using the derivative. Substitute:

Evaluate:

Then by the point-slope form:

Yields:

Distribute:

Hence, our equation is:

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