设y=y(x)是方程xˆ2eˆy+yˆ2=1确定函数,求dy/dx│(1,0)
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![设y=y(x)是方程xˆ2eˆy+yˆ2=1确定函数,求dy/dx│(1,0)](/uploads/image/z/5411831-23-1.jpg?t=%E8%AE%BEy%3Dy%28x%29%E6%98%AF%E6%96%B9%E7%A8%8Bx%26%23710%3B2e%26%23710%3By%2By%26%23710%3B2%3D1%E7%A1%AE%E5%AE%9A%E5%87%BD%E6%95%B0%2C%E6%B1%82dy%2Fdx%E2%94%82%281%2C0%29)
设y=y(x)是方程xˆ2eˆy+yˆ2=1确定函数,求dy/dx│(1,0)
设y=y(x)是方程xˆ2eˆy+yˆ2=1确定函数,求dy/dx│(1,0)
设y=y(x)是方程xˆ2eˆy+yˆ2=1确定函数,求dy/dx│(1,0)
x^2e^y+y^2=1
两边对x求导得2xe^y+x^2e^y*y'(x)+2y*y'(x)=0
故y'(x)=-2xe^y/(x^2e^y+2y)
所以dy/dx│(1,0)=-2*1*e^0/(1^2*e^0+2*0)=-2
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