VERY URGENT!!! really need help with these partial derivatives immediately

no matter what I am trying, whether product rule, quotient rule, etc, I cannot get the correct answer!!

1) z=(x+y)e^x, find partial derivative of z with respect to x, and then with respect to y.

2) z=cos(y/x), find partial derivative of z with respect to x, and then with respect to y.

I can't write "partial" signs with my keyboard, so I'll just write dz/dx for "partial of z w/r/t x".

(1) dz/dx = (x+y)e^x + e^x; dz/dy = e^x

(2) dz/dx = (y/x^2) sin(y/x) ; dz/dy = -(1/x) sin(y/x)

1) dz/dx = (x+y)e^x + (1+y)e^x

dz/dy = (x+y)*0 + (x+1)e^x = (x+1)e^x

2) dz/dx = -sin(y/x)(-yx^(-2)

dz/dy = -sin(y/x)*(1/x)

Jen