y=ln√(x(x+2)/(x+3))的导数：根号里x(x+2)是分子,x+3是分母,

网友回答

y=ln√(x(x+2)/(x+3))
y'=[1/√(x(x+2)/(x+3))]*[√(x(x+2)/(x+3))]'
=(1/2)*1/[√(x(x+2)/(x+3))]^2*[(x(x+2)/(x+3)]'
=(x+3)/[2x(x+2)]*[(x(x+2)/(x+3)]'
[x(x+2)/(x+3)]'
={[x(x+2)]'*(x+3)-x(x+2)*(x+3)'}/(x+3)^2
=(x^2+6x+6)/(x+3)^2
所以y'=(x^2+6x+6)/[2x(x+2)(x+3)]