对x：du/dx=x/√(x2+y2+z2)对y：du/dy=y/√(x2+y2+z2)对z：du/dz=z/√(x2+y2+z2)在 xOy 平面内，当动点由 P(x0,y0) 沿不同方向变化时，函数 f(x,y) 的变化快慢一般来说是不同的，因此就需要研究 f(x,y) 在 (x0,y0) 点处沿不同方向的变化率。
1、 设u=f(x2+y2+z2.xyz)求偏导数过程，见上图第一张图。2、 u=f(x2+y2+z2.xyz)求偏导数，用的是复合函数求导法则，即第二张图公式的推广，即二个中间变量的，最终三个自变量。具体的求u=f(x2+y2+z2.xyz)偏导数的解答见上。
对x求导：yz+xyz'x+(x+zz'x)/p=0, 得：z'x=-(yz+x/p)/(xy+z/p)同样,对y求导,得：z'y=-(xz+y/p)/(xy+z/p)所以在(1,0,-1)处,有p=√2 z'x=-(1/p)/(-1/p)=1 z'y=-(-1)/(-1/p)=-1/p=-√2/2 所以dz=z'xdx+z'ydy=dx-√2/2*dy ...
把y^2=z-x^2代入x^2+2y^2+3z^2=20中得到3z^2+2z-x^2-20=0 求导6z*z'+2*z'-2x=0,（其中z'表示z关于x的导数,本来应该有别的写法的,但是表示不便,所以这么写了）,z'=2x,代入上面那个就ok了
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Position, Euler angle, linear velocity, and angular velocity are among the 12-degree-of-freedom output states described by Equation (2). 12−𝐷𝑂𝐹=[𝑥,𝑦,𝑧,𝜙,𝜃,𝜓,𝑥˙,𝑦˙,𝑧˙,𝜙˙,𝜃˙,𝜓˙]12−DOF=[x,y,z,ϕ,θ,ψ,x˙,y˙,z˙,ϕ˙,θ...