求y导数,
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求y导数,
![](http://img.wesiedu.com/upload/7/25/725bb0cb2fe5ea7b4ea9af7e6ab3f001.jpg)
![](http://img.wesiedu.com/upload/7/25/725bb0cb2fe5ea7b4ea9af7e6ab3f001.jpg)
![求y导数,](/uploads/image/z/16609417-25-7.jpg?t=%E6%B1%82y%E5%AF%BC%E6%95%B0%2C)
记:u(x)=√(x^2+1) (1)
原题:y=(u-x)/(u+x) (2)
u的导数:u' = x/u (3)
y的导数:y' = [(u'-1)(u+x)-(u-x)(u'+1)]/(u+x)^2
y' = 2(x^2-u^2)/[u(u+x)^2] (4)
将 u 代入y'
最后得到:y' =-2/{√(x^2+1) [√(x^2+1)+x]^2} (5)
原题:y=(u-x)/(u+x) (2)
u的导数:u' = x/u (3)
y的导数:y' = [(u'-1)(u+x)-(u-x)(u'+1)]/(u+x)^2
y' = 2(x^2-u^2)/[u(u+x)^2] (4)
将 u 代入y'
最后得到:y' =-2/{√(x^2+1) [√(x^2+1)+x]^2} (5)