Final answer:
To find y' in the equation 2x² - y² = 3 by implicit differentiation, differentiate both sides of the equation with respect to x. By applying the product rule and simplifying the equation, we can isolate y' and find the answer.
Step-by-step explanation:
To find y' by implicit differentiation, we differentiate both sides of the equation with respect to x. Since 2x² is the same as 2x² * 1 and -y² is the same as -1 * y², we can use the product rule. Differentiating 2x² with respect to x gives us 4x, and differentiating -y² with respect to x gives us -2yy'. Plugging these derivatives back into the equation, we get 4x - 2yy' = 0. To find y', we can isolate it by moving the terms without y' to the other side of the equation. Doing so, we get y' = (4x)/(2y) = 2x/y.