x/x^2+y^2的x一阶偏导数,要详细说明怎么来的,我困扰好久了,拜托了,大家~~~

Question

x/x^2+y^2 的x一阶偏导数,要详细说明怎么来的,我困扰好久了,拜托了,大家~~~

Answer 1

函数商求导：
令u(x)=x²+y²
z=x/u(x)
=[x'u(x)-x*u'(x)]
=(x²+y²-x*2x)/(x²+y²)²
=(y²-x²)/(x²+y²)²