求达人解高数习题设y=f(x)是方程xy-e^x+e^y=0确定的隐函数,求dy/dx
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求达人解高数习题
设y=f(x)是方程xy-e^x+e^y=0确定的隐函数,求dy/dx
设y=f(x)是方程xy-e^x+e^y=0确定的隐函数,求dy/dx
![求达人解高数习题设y=f(x)是方程xy-e^x+e^y=0确定的隐函数,求dy/dx](/uploads/image/z/16871748-60-8.jpg?t=%E6%B1%82%E8%BE%BE%E4%BA%BA%E8%A7%A3%E9%AB%98%E6%95%B0%E4%B9%A0%E9%A2%98%E8%AE%BEy%3Df%28x%29%E6%98%AF%E6%96%B9%E7%A8%8Bxy-e%5Ex%2Be%5Ey%3D0%E7%A1%AE%E5%AE%9A%E7%9A%84%E9%9A%90%E5%87%BD%E6%95%B0%2C%E6%B1%82dy%2Fdx)
xy-e^x+e^y=0
方程两边同时对x求导:
(x)′·y+x·(y)′-e^x+e^y·y′=0
∴y+x·dy/dx-e^x+e^y·dy/dx=0
∴dy/dx=(e^x-y)/(x+e^y)
方程两边同时对x求导:
(x)′·y+x·(y)′-e^x+e^y·y′=0
∴y+x·dy/dx-e^x+e^y·dy/dx=0
∴dy/dx=(e^x-y)/(x+e^y)
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