Final answer:
To find y', differentiate both sides of the equation with respect to x. Set the derivative equal to zero and solve for dy/dx.
Step-by-step explanation:
To find y', we will differentiate both sides of the equation with respect to x. Let's differentiate term by term.
Differentiating 6x² with respect to x gives us 12x. Differentiating -y² with respect to x gives us -2y * dy/dx (chain rule).
Setting the derivative of 6x² - y² equal to 0 gives us 12x - 2y * dy/dx = 0. Rearranging this equation, we get dy/dx = (12x)/(2y).