求函数u=x2+y2+z2在椭球面x2/a2+y2/b2+z2/c2＝1上点M.(X.,Y.,Z.)处沿外法线的方向导数

设F=x^2/a^2+y^2/b^2+z^2/c^2-1
则其法线方向为：(Fx,Fy,Fz)=(2x/a²,2y/b²,2z/c²),此方向就是外法线方向
将(2x/a²,2y/b²,2z/c²)化为单位向量得：(x/a²,y/b²,z/c²)/√(x²/a^4+y²/b^4+z²/c^4)
即cosα=(x/a²)/√(x²/a^4+y²/b^4+z²/c^4)
cosβ=(y/b²)/√(x²/a^4+y²/b^4+z²/c^4)
cosγ=(z/c²)/√(x²/a^4+y²/b^4+z²/c^4)
u=x^2+y^2+z^2的方向导数为：
du/dx*cosα+du/dy*cosβ+du/dz*cosγ
=2x*(x/a²)/√(x²/a^4+y²/b^4+z²/c^4)+2y*(y/b²)/√(x²/a^4+y²/b^4+z²/c^4)
+2z*(z/c²)/√(x²/a^4+y²/b^4+z²/c^4)
=2(x²/a²+y²/b²+z²/c²)/√(x²/a^4+y²/b^4+z²/c^4)
由于x^2/a^2+y^2/b^2+z^2/c^2=1
=2/√(x²/a^4+y²/b^4+z²/c^4)

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