Question

求ln[(1+3x^2)/(2-x^2)]导数

Answer 1

ln[(1+3x^2)/(2-x^2)]

复合函数求导

y'=[(2-x^2)/(1+3x^2)]*[(1+3x^2)/(2-x^2)]'

==[(2-x^2)/(1+3x^2)]*[(1+3x^2)'*(2-x^2)-(1+3x^2)*(2-x^2)']/(2-x^2)^2

=[6x(2-x^2)+2x(1+3x^2)]/(2-x^2)(1+3x^2)

=14x/(2-x^2)(1+3x^2)