1. The problem statement, all variables and given/known data Find the unit vector with positive z component which is normal to the surface z = x^2*y + x*y^4 at the point (1,1,2) on the surface 3. The attempt at a solution So I find: dz/dx = 2xy +y^4 dz/dy = x^2 + 4xy^3 Substitute (1,1) in those equations and get dz/dx = 3, and dz/dy = 5 So now we have (3, 5, -1) Multiply by -1 and now we have (-3, -5, 1), but it's apparently wrong. However the answer was (-3/35*sqrt(35), -1/7*sqrt(35), 1/35*sqrt(35)) I haven't the faintest idea as to how that came about, well...it seems to have been multiplied by sqrt(35)/35, except for the second component which appears to have something else done to it. I looked around for how the normal vector is calculated in my book, and online too; it's pretty much what I've done.