Finding equation of tangent plane & normal line to a given surface

[physicsidiot1]

Homework Statement

Find equations of the tangent plant and the normal line to x-z=4arctan(yz) at (1+∏, 1, 1)

Homework Equations

The Attempt at a Solution

I took the partials and got f_x=0 f_y=0 f_z=(-4y)/((yz)²+1) so for the plane i got -2z-2=0 and for the normal line I got .5z-2=0. I feel like I may have messed up somewhere, probably in taking the partials...

 

[LCKurtz]

Homework Statement

Find equations of the tangent plant and the normal line to x-z=4arctan(yz) at (1+∏, 1, 1)

Homework Equations

The Attempt at a Solution

I took the partials and got f_x=0 f_y=0 f_z=(-4y)/((yz)²+1) so for the plane i got -2z-2=0 and for the normal line I got .5z-2=0. I feel like I may have messed up somewhere, probably in taking the partials...

Start by writing your function like this:

f(x,y,z) = x - z - 4arctan(yz) = 0

Then look again at your partials (they are all three wrong). In particular, for example, how do you get f_x = 0 out of that, for starters? Show us what you get for your normal vector then we can talk.

 

[HallsofIvy]

When I look at x- z= 4 arctan(yz), I see both x and y variables in it. So the derivatives f_x and f_y can't be 0.

But since you never say exactly what "f" is, it is impossible to tell what you are doing.