由商的求导公式可以知道,
y'
={(1+3x)' * [√4+5(x^2)] -(1+3x) *[√4+5(x^2)]' } / [√4+5(x^2)]^2
显然(1+3x)'=3,而[√4+5(x^2)]' = 10x / 2*[√4+5(x^2)]= 5x / [√4+5(x^2)]
所以
y'
={3* [√4+5(x^2)] -(1+3x) *5x / [√4+5(x^2)] } / [4+5(x^2)]
=(12-5x) / [4+5(x^2)]^(3/2)