Find the linear approximation of (xy)/z at the point (-3,2,1)
The Attempt at a Solution
So the example my book gives has 2 variables so i'm struggling a bit with this, But I started off by taking the partial derivative with respect to each variable and solving for it.
d/dx = (y/z) = 2 = A
d/dy = (x/z) = -3 = B
d/dz = -(xy)/z^2 =6 = C
now... find the equation of a plane passing through that point maybe?
A(x-xo)+B(y-yo)+C(z-zo) = 0
2(x+3) - 3(y-2) + 6(z-1) = 0
2x+6 - 3y+6 +6z-6 = 0
am I on the right track here..?