cos(wt)*e^(st)对t的导数求解要求详细说明,苦恼
问题描述：
cos(wt)*e^(st)对t的导数求解
要求详细说明,苦恼
答
运用乘积的求导法则：(f*g)'=f'*g+f*g',以及复合函数求到法则
可知[cos(wt)*e^(st)]'=[cos(wt)]'*e^(st)+cos(wt)*[e^(st)]'
=-w*sin(wt)*e^(st)+cos(wt)*s*e^(st)=e^(st)*[-w*sin(wt)+s*cos(wt)]
答
cos(wt)*e^(st)对t的导数=cos(wt)对t的导数乘以e^(st)+e^(st)对t的导数乘以cos(wt)=-wsin(wt)*e^(st)+s*e^(st)*cos(wt)
cos(wt)对t的导数=[-sin(wt)]*w
答
cos(wt)*e^(st)符合函数求导
[cos(wt)*e^(st)]'=cos(wt)'*e^(st)+cos(wt)*e^(st)'
=-wcos(wt)*e^(st)+cos(wt)*s*e^(st)
=cos(wt)*e(st)*(s-w)
答
[cos(wt)*e^(st)]'
=[cos(wt)]'*e^(st)+cos(wt)*[e^(st)]'
=-sin(wt)*(wt)'*e^(st)+cos(wt)*e^(st)*(st)'
=-w*sin(wt)*e^(st)+s*cos(wt)*e^(st)
=e^(st)[s*cos(wt)-w*sin(wt)]