题目

y=xarctan根号下x的微分,还有y=lntan二分之x的微分

提问时间：2021-02-21

答案

y=xarctan根号下x
dy=arctan√x*dx+x*darctan√x
=arctan√xdx+x*1/(1+x)*1/2√x*dx
=[arctan√x+√x/2(1+x)]dx
dy=dlntan(x/2)
=1/tan(x/2)*sec^2(x/2)*1/2*dx
=sec^2(x/2)/2tan(x/2)*dx