ln(tan(x/2))的导数怎么得到1/sinx的呢?

问题描述:

ln(tan(x/2))的导数怎么得到1/sinx的呢?

(ln(tan(x/2)))'=1/tan(x/2)*(tan(x/2))'
=1/tan(x/2)*1/cos^2(x/2)*(x/2)'
=1/(sin(x/2)cos(x/2))*1/2
=1/(2sin(x/2)cos(x/2))
=1/sinx