Answer
$z_x=-5x^4y^4sin(x^5y^4)$
$z_y=-4x^5y^3sin(x^5y^4)$
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:
$z_x=-sin(x^5y^4)*5x^4y^4=-5x^4y^4sin(x^5y^4)$
$z_y=-sin(x^5y^4)*4x^5y^3=-4x^5y^3sin(x^5y^4)$
