求第六题的隐函数y=y(x)的导数
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求第六题的隐函数y=y(x)的导数
![](http://img.wesiedu.com/upload/a/c9/ac9009ea0d8d4fd16eabb9bf37ce6783.jpg)
![](http://img.wesiedu.com/upload/a/c9/ac9009ea0d8d4fd16eabb9bf37ce6783.jpg)
![求第六题的隐函数y=y(x)的导数](/uploads/image/z/17444863-55-3.jpg?t=%E6%B1%82%E7%AC%AC%E5%85%AD%E9%A2%98%E7%9A%84%E9%9A%90%E5%87%BD%E6%95%B0y%3Dy%28x%29%E7%9A%84%E5%AF%BC%E6%95%B0)
两边对x求导:
y'sinx+ycosx+sin(x-y) (1-y')=0
y'=-[ycosx+sin(x-y)]/[sinx-sin(x-y)]
当x=0时,代入原方程,得;0-cos(0-y)=0,得:cosy=0,只取其一个主值,y(0)=π/2
所以y'(0)=-[π/2+sin(-π/2)]/[0-sin(-π/2)]=1-π/2
y'sinx+ycosx+sin(x-y) (1-y')=0
y'=-[ycosx+sin(x-y)]/[sinx-sin(x-y)]
当x=0时,代入原方程,得;0-cos(0-y)=0,得:cosy=0,只取其一个主值,y(0)=π/2
所以y'(0)=-[π/2+sin(-π/2)]/[0-sin(-π/2)]=1-π/2