.高数题 已知函数z=(1/3)ln(x-y),x=sect,y=3 sint 求（dz/dt) | t=π
问题描述：
.高数题 已知函数z=(1/3)ln(x-y),x=sect,y=3 sint 求（dz/dt) | t=π
答
dx/dt=tantsect dy/dt=3cost
dz/dt=(∂z/∂x)(dx/dt)+(∂z/∂y)(dy/dt)
=(tantsect)/[3(x-y)]-(3cost)/[3(x-y)]
=(tantsect-3cost)/[3(sect-3sint)]
将t=π代进去
dz/dt=3/(-3)=-1
希望对你有帮助
答
z=(1/3)ln(sect-3sint)
dz/dt=(1/3)(secttant-3cost)/(sect-3sint)
t=π
dz/dt=(1/3)(3)/(1）=1