已知 x = e^t * cos t y = e^t *sin t 求当t= π/3时dy/dx的值

题目

已知 x = e^t * cos t y = e^t *sin t 求当t= π/3时dy/dx的值

答案

dy/dx=(e^t×sint)′/(e^t×cost)′
=(e^t×sint+cost×e^t)/(e^t×cost-sint×e^t)
=(sint+cost)/(cost-sint)
当x=π/3
=(根号下3/2+1/2)/(1/2-根号下3/2)
=-2-根号下3