y=(x+3)/(x^2+3)
y'=[(x+3)'(x^2+3)-(x+3)(x^2+3)']/(x^2+3)^2
=[(x^2+3)-2x(x+3)]/(x^2+3)^2
=[x^2+3-2x^2-6x]/(x^2+3)^2
=(-x^2-6x+3)/(x^2+3)
用两函数之商的求导法则求y=x+3/x^2+3的导数
y=(x+3)/(x^2+3)
y'=[(x+3)'(x^2+3)-(x+3)(x^2+3)']/(x^2+3)^2
=[(x^2+3)-2x(x+3)]/(x^2+3)^2
=[x^2+3-2x^2-6x]/(x^2+3)^2
=(-x^2-6x+3)/(x^2+3)