x^y=y^x的导数 答案为什么是y'=y^2(Inx-1)/x^2(Iny-1)啊?我算是y'=(iny-y/x)/(Inx-x/y)?
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![x^y=y^x的导数 答案为什么是y'=y^2(Inx-1)/x^2(Iny-1)啊?我算是y'=(iny-y/x)/(Inx-x/y)?](/uploads/image/z/2625210-18-0.jpg?t=x%5Ey%3Dy%5Ex%E7%9A%84%E5%AF%BC%E6%95%B0+%E7%AD%94%E6%A1%88%E4%B8%BA%E4%BB%80%E4%B9%88%E6%98%AFy%27%3Dy%5E2%28Inx-1%29%2Fx%5E2%28Iny-1%29%E5%95%8A%3F%E6%88%91%E7%AE%97%E6%98%AFy%27%3D%28iny-y%2Fx%29%2F%28Inx-x%2Fy%29%3F)
x^y=y^x的导数 答案为什么是y'=y^2(Inx-1)/x^2(Iny-1)啊?我算是y'=(iny-y/x)/(Inx-x/y)?
x^y=y^x的导数 答案为什么是y'=y^2(Inx-1)/x^2(Iny-1)啊?我算是y'=(iny-y/x)/(Inx-x/y)?
x^y=y^x的导数 答案为什么是y'=y^2(Inx-1)/x^2(Iny-1)啊?我算是y'=(iny-y/x)/(Inx-x/y)?
ylnx=xlny
对x求导
y'lnx+y*1/x=lny+x*1/y*y'
(lnx-x/y)y'=lny-y/x
y'=(lny-y/x)/(lnx-x/y)
ylnx=xlny
lnx=xlny/y,lny=ylnx/x
代入y'=(lny-y/x)/(lnx-x/y)
然后上下乘xy即可