什么是对数微分,
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什么是对数微分,
![什么是对数微分,](/uploads/image/z/18670495-31-5.jpg?t=%E4%BB%80%E4%B9%88%E6%98%AF%E5%AF%B9%E6%95%B0%E5%BE%AE%E5%88%86%2C)
是求微分的一种方法,办法是:先取对数,再求导数,以使算法简便
比如,
设y=((x+2)^2/((x-5)(x+3))^(1/3),求y'
两边取对数,得:
lny=(1/3)(2ln(x+2)-ln(x-5)-ln(x+3))
两边求导,得:
(1/y)y'=(1/3)(2/(x+2)-1/(x-5)-1/(x+3))
y'=(y/3)(2/(x+2)-1/(x-5)-1/(x+3))
=(1/3)((x+2)^2/((x-5)(x+3))^(1/3))(2/(x+2)-1/(x-5)-1/(x+3))
比如,
设y=((x+2)^2/((x-5)(x+3))^(1/3),求y'
两边取对数,得:
lny=(1/3)(2ln(x+2)-ln(x-5)-ln(x+3))
两边求导,得:
(1/y)y'=(1/3)(2/(x+2)-1/(x-5)-1/(x+3))
y'=(y/3)(2/(x+2)-1/(x-5)-1/(x+3))
=(1/3)((x+2)^2/((x-5)(x+3))^(1/3))(2/(x+2)-1/(x-5)-1/(x+3))