1. implicit differientiation

Use implicit differentiation to find dz/dx and dz/dy.
xyz = cos(x + y + z)

2. We are looking for partial derivatives let dz/dx be the partial derivative of z wrt x

For dz/dx think of z = f(x,y)

xyz = cos(x + y + z)

yz + xydz/dx = sin(x+y+z)(1 + dz/dx)

For dz/dy think y = f(x,z)

yz + xzdz/dx = sin(x+y+z)(1 + dz/dx)