f(x,y) = x^2 + 4y^2
fx'(x,y) = 2x;
fy'(x,y) = 8y;
f(2,1) = 8 = z0;
fx'(2,1) = 4;
fy'(2,1) = 8;
tangent plane (2,1):
z-8 = 4(x-2)+(y-1)
formula
P(x0,y0,z0)
F(x,y,z) =^ surface
z-z0 = fx'(x0,y0)(x-x0)+fy'(x0,y0)(y-y0)
// cos
x0 =^ x;
y0 =^ y;
z0 =^ f(x,y);
f(x,y) = sin(x/3)+sin(y/3);
fx'(x,y) = cos(x/3)
fy'(x,y) = cos(y/3)
zä-sin(x/3)-sin(y/3) = cos(x/3)(xä-x)+cos(y/3)(yä-y)
zä = cos(x/3)(xä-x)+cos(y/3)(yä-y)+sin(x/3)+sin(y/3)
zä = xä*cos(x/3) - x*cos(x/3) + yä*cos(y/3) - y*cos(y/3) + sin(x/3) + sin(y/3)
sin(x/3) + sin(y/3) - x*cos(x/3) - y*cos(y/3) = -cos(x/3)*xä -cos(y/3)*yä + zä
N = [-cos(x/3),-cos(y/3),1]