Final answer:
The question appears to contain a typo in the equation provided. Assuming a corrected version of the equation is 3y² = 5x - 2, implicit differentiation yields dy/dx = 5/(6y), provided that y is not zero.
Step-by-step explanation:
The question asks us to use implicit differentiation to find dy/dx for the equation 3y² = 5 - 2/5 - 2. There appears to be a typo in the equation, which should likely be 3y² = 5x - 2 or something similar. Assuming the equation is 3y² = 5x - 2, we differentiate both sides with respect to x:
6y(dy/dx) = 5.
Then, solving for dy/dx gives:
dy/dx = 5/(6y).
If y is not zero, this equation gives the value of dy/dx for the curve at any point (x, y). However, if the equation provided is complete as stated, then implicit differentiation cannot be performed due to the constant nature of the right side.