Find the correct values for \(\frac{∂f}{∂x} \,and\, \frac{∂f}{∂y}\) for the function \(f=\frac{2}{x^3}y^2+4y^3.\)

• A. \(\frac{∂f}{∂x}= \frac{-6}{x^2}, \frac{∂f}{∂y}= \frac{2}{x^3} y+8y^2\)
• B. \(\frac{∂f}{∂x}= \frac{2}{x^4}, \frac{∂f}{∂y}= \frac{2}{x^3} y+12y^2\)
• C. \(\frac{∂f}{∂x}= \frac{-6}{x^4}, \frac{∂f}{∂y}= \frac{4}{x^3} y+12y^2\)
• D. \(\frac{∂f}{∂x}= \frac{-6}{x^4}, \frac{∂f}{∂y}= \frac{4}{x^3} y^2+12\)