Final answer:
To find y' by implicit differentiation for the equation 8x² - y² = 6, the derivative of 8x² - y² is 16x - 2yy'. Solving for y', we have y' = 4x/y.
Step-by-step explanation:
To find y' by implicit differentiation for the equation 8x² - y² = 6, we differentiate both sides of the equation with respect to x. For the left side, we use the chain rule since there is a y variable. For the right side, the derivative of a constant is 0. So, the derivative of 8x² - y² is 16x - 2yy'. Setting this equal to 0, we get 16x - 2yy' = 0. Solving for y', we have y' = 8x/2y = 4x/y. Therefore, y' = 4x/y.