求ln[(1+3x^2)/(2-x^2)]导数

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求ln[(1+3x^2)/(2-x^2)]导数

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

求ln[(1+3x^2)/(2-x^2)]导数
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)