Chapter 14: Partial Derivatives - Section 14.3 - Partial Derivatives - Exercises 14.3 - Page 807: 8

$f_x=2/3(x^3+y/2)^{-1/3}\times 3x^2$ $f_y=2/3(x^3+y/2)^{-1/3}\times 1/2$

Take the first partial derivatives of the given function. When taking a partial derivative with respect to x, treat y as a constant, and vice versa: $f_x=2/3(x^3+y/2)^{-1/3}\times 3x^2$ $f_y=2/3(x^3+y/2)^{-1/3}\times 1/2$