f'(x)=e^x+xe^x+(sinx/x -lnxcosx)/(sinx)^2
当x=π/2时,
f(π/2)=π/2e^(π/2)+ln(π/2) →切点的纵坐标
f'(π/2)=e^(π/2)(π/2+1)+2/π →切线的斜率
切线方程为y-f(π/2)=f'(π/2)(x-π/2) →点斜式
你自己带入计算就可得出切线方程.