高数 求下列由方程所确定的隐函数y=y(x)的导数dy/dx1.(1)x^4-y^4=4-4xy(2)acrtan(y/x)=ln根号下(x^2+y^2)2.求曲线x^3+3xy+y^3=5在点(1,1)处的切线方程和法线方程
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![高数 求下列由方程所确定的隐函数y=y(x)的导数dy/dx1.(1)x^4-y^4=4-4xy(2)acrtan(y/x)=ln根号下(x^2+y^2)2.求曲线x^3+3xy+y^3=5在点(1,1)处的切线方程和法线方程](/uploads/image/z/1826683-43-3.jpg?t=%E9%AB%98%E6%95%B0+%E6%B1%82%E4%B8%8B%E5%88%97%E7%94%B1%E6%96%B9%E7%A8%8B%E6%89%80%E7%A1%AE%E5%AE%9A%E7%9A%84%E9%9A%90%E5%87%BD%E6%95%B0y%3Dy%28x%29%E7%9A%84%E5%AF%BC%E6%95%B0dy%2Fdx1.%281%29x%5E4-y%5E4%3D4-4xy%282%29acrtan%28y%2Fx%29%3Dln%E6%A0%B9%E5%8F%B7%E4%B8%8B%28x%5E2%2By%5E2%292.%E6%B1%82%E6%9B%B2%E7%BA%BFx%5E3%2B3xy%2By%5E3%3D5%E5%9C%A8%E7%82%B9%281%2C1%29%E5%A4%84%E7%9A%84%E5%88%87%E7%BA%BF%E6%96%B9%E7%A8%8B%E5%92%8C%E6%B3%95%E7%BA%BF%E6%96%B9%E7%A8%8B)
高数 求下列由方程所确定的隐函数y=y(x)的导数dy/dx1.(1)x^4-y^4=4-4xy(2)acrtan(y/x)=ln根号下(x^2+y^2)2.求曲线x^3+3xy+y^3=5在点(1,1)处的切线方程和法线方程
高数 求下列由方程所确定的隐函数y=y(x)的导数dy/dx
1.(1)x^4-y^4=4-4xy
(2)acrtan(y/x)=ln根号下(x^2+y^2)
2.求曲线x^3+3xy+y^3=5在点(1,1)处的切线方程和法线方程
高数 求下列由方程所确定的隐函数y=y(x)的导数dy/dx1.(1)x^4-y^4=4-4xy(2)acrtan(y/x)=ln根号下(x^2+y^2)2.求曲线x^3+3xy+y^3=5在点(1,1)处的切线方程和法线方程
1、(1)两边对x求导得:
4x³-4y³y'=-4y-4xy'
解得:y'=(x³+y)/(y³-x)
(2)方程化为:arctan(y/x)=(1/2)ln(x²+y²)
两边对x求导得:(y/x)'/[1+(y/x)²]=(x+yy')/(x²+y²)
即:[(xy'-y)/x²]/[1+(y/x)²]=(x+yy')/(x²+y²)
即:(xy'-y)/(x²+y²)=(x+yy')/(x²+y²)
得:xy'-y=x+yy'
解得:y'=(x+y)/(x-y)
2、两边对x求导得:3x²+3y+3xy'+3y²y'=0
消去3,将x=1,y=1代入得:1+1+y'+y'=0,解得:y'=-1
切线方程:y-1=-(x-1),即:y=-x+2
法线方程:y-1=x-1,即:y=x
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