Answer
$z_x=8(2x+5)(x^2+5x-2y)^7$
$z_y=-16(x^2+5x-2y)^7$
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:
$z_x=8(x^2+5x-2y)^7*(2x+5*1-0)=8(2x+5)(x^2+5x-2y)^7$
$z_y=8(x^2+5x-2y)^7*(0+0-2*1)=-16(x^2+5x-2y)^7$
