Answer
$f_x=12x^5+2y$
$f_y=8y^7+2x$
Work Step by Step
Take the first partial derivatives of the given function. When taking partial derivative with respect to x, treat y as a constant, and vice versa:
$f_x=0+ 12x^5+2y=12x^5+2y$
$f_y=8y^7+0+2x=8y^7+2x$
