设z=z(t)由x+y-z=e^z,xe^x=tan t,y=cos t所确定,求dz/dt/t=0

题目

设z=z(t)由x+y-z=e^z,xe^x=tan t,y=cos t所确定,求dz/dt/t=0
给出详细过程

答案

x,y,z都是t的函数,记作x(t),y(t),z(t)（1）首先求出x(0),y(0),z(0)t = 0,x(0)e^x(0)=tan 0 = 0e^x(0) > 0,则 x(0) = 0y(0) = cos 0 = 1x(0)+y(0)-z(0)=e^z(0)得到e^z(0) + z(0) -1 = 0为求z(0),即解方程 e^z + z -1 ...