设z=f(x,y)是由方程z=x+ysin(z)所确定的隐函数,则dz⼀dx=

谢谢了!
2025-04-07 23:32:47
推荐回答(2个)
回答1:

z = x + ysin(z) 两边对x求偏导
∂z/∂x = 1 + ycos(z) ∂z/∂x
∂z/∂x {1 - ycos(z)} = 1
解出:∂z/∂x = 1/{1 - ycos(z)}

回答2:

两边取全微分即可
dz=dx+sinzdy+ycoszdz
所以
dz=dx /(1-ycosz)+sinzdy /(1-ycosz)
所以dz/dz=1/(1-ycosz)