7. (a) Use implicit differentiation to find dy/dx for the curve x³ + y³ = 3xy (b) Find an equation for the tangent line to the curve in (a) at the point (3/2, 3/2)
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The derivative of x^3 is 3x^2. The derivative of y^3 is 3y^2 * dy/dx (by the chain rule, since y is a function of x). The derivative of 3xy is 3y + 3x * dy/dx (by the product rule). So, differentiating both sides of the equation gives us: 3x^2 + 3y^2 * Show more…
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