I have the following equation:

z (x y)= 200 + 1/100(x^2 - 4xy + 3y^2)

I need to find the partial derivatives in order to find grad z.

After expanding the brackets out I got the partial derivatives as:

dz/dx = (1/50x - 1/25y)

dz/dy = (1/25x + 3/50y)

Thus giving me grad z as:

(1/50x - 1/25y) + (1/25x + 3/50y)

Is this right?