Final answer:
To find the derivative dy/dx when applying implicit differentiation to the equation x² + y² = 8, we differentiate both sides of the equation with respect to x. Then, we rearrange the equation to solve for dy/dx.
Step-by-step explanation:
To find the derivative, we need to apply implicit differentiation to the equation x² + y² = 8. We differentiate both sides of the equation with respect to x. The derivative of x² is 2x and the derivative of y² with respect to x is 2yy'. Therefore, the derivative of the left side is 2x + 2yy'.
The derivative of the right side is 0 since it is a constant. So, 2x + 2yy' = 0. Rearranging the equation to solve for dy/dx, we get dy/dx = -x/y.