利用对数求导法求y=(x-1)(x-2)²(x-3)³导数 要过程,谢谢
所以 y'=y*[1\/(x-1) +2\/(x-2)+3\/(x-3)]代入y=(x-1)(x-2)²(x-3)³所以 y'=(x-2)²(x-3)³ + 2(x-1)(x-2)(x-3)³+3(x-1)(x-2)²(x-3)²
请问一题求导题
y=(x-1)(x-2)(x-3);求y'=?解:用对数求导法:lny=ln(x-1)+ln(x-2)+ln(x-3);y'\/y=1\/(x-1)+1\/(x-2)+1\/(x-3);∴y'=y[1\/(x-1)+1\/(x-2)+1\/(x-3)]=(x-1)(x-2)(x-3)[1\/(x-1)+1\/(x-2)+1\/(x-3)];...
等式两边同时取对数,什么条件下能同时取对数??
1、已知y=(x+1)³(x-2)²,求导数。解:对等式两边同时取对数得:lny=3ln(x+1)+2ln(x-2)两边同时对x求导有:y'\/y=3\/(x+1)+2\/(x-2)所以,y'=[3\/(x+1)+2\/(x-2)]*[(x+1)³(x-2)²]=3(x+1)²(x-2)²+2(x+1)³(x-2...
微积分问题怎么知道求导的时候要用两边取对数的方法
两边对x求导:y'\/y = 2sinxcos+2cosxsinsinx = 2sin(2x)y' = 2sin(2x) e^(sin²x-cos²x)再举一例:y= x^x 求y'两边取对数:lny = xlnx 两边对x求导:y'\/y =lnx+1 解出:y' = (1+lnx)x^x 用两边取对数方法求导要比用复合 函数链式法层次清楚,不宜出...
1.利用对数求导法求导:y=[(x-1)x(x+1)(x+2)\/(x-2)^2(...
1.两边分别求导,左边=(lny)'=y'lny,右边对数乘除可以化为加减,这样方便求导,左右相等就可以得到结果.你那式子写的存在歧义,把正确的式子自己算下就好了.2.同上求得y',再计算y"
求y=√{[(x-1)(x-2)]\/[(x-3)(x-4)]}的导数, 看不到回答,怎么搞的
取对数,得lny=1\/2 [ln|x-1|+ln|x-2|-ln|x-3|-ln|x-4|]两边求导,得y'\/y=1\/2×【1\/(x-1)+1\/(x-2)-1\/(x-3)-1\/(x-4)】y'=y×1\/2×【1\/(x-1)+1\/(x-2)-1\/(x-3)-1\/(x-4)】y'=√{[(x-1)(x-2)]\/[(x-3)(x-4)]}×1\/2×【1\/(x-1)...
对数求导法求导问题?
ln(x^y)=y*lnx lny=ln{[(x^2)\/(x^2-1)]*[(x+2)\/(x-2)^2]^(1\/3)} =ln(x^2)-ln(x^2-1)+ln(x+2)^(1\/3)-ln(x-2)^2^(1\/3)=2lnx - ln(x^2-1) + [ln(x+2) ]\/3- 2[ln(x-2)]\/3 自然对数:以e为底的对数,表示为ln=loge x² 取自然对数:...
求y=√{[(x-1)(x-2)]\/[(x-3)(x-4)]}的导数,谢谢。
取对数即可,答案如图所示
1.利用对数求导法求导:y=[(x-1)x(x+1)(x+2)\/(x-2)^2(x+3)]^1\/3 2...
y'=1\/3[1\/(x-1)+1\/x+1\/(x+1)+1\/(x+2)-2\/(x-2)-1\/(x+3)][(x-1)x(x+1)(x+2)\/(x-2)^2(x+3)]^1\/3 2.y'=10(x^2-2x+5)^9(2x-2)=20(x^2-2x+5)^9(x-1)y"=20[(x^2-2x+5)^9]'(x-1)+20(x^2-2x+5)^9[(x-1)]'=20[9(x^2-2x+5)^...
求一道数学导数题 设f(x)=(x-1)(x-2)...(x-2011).求f'(x)
用对数求导法:取 ln|f(x)| =∑(1≤k≤2011)ln|x-k|,求导,得 f'(x)\/f(x) =∑(1≤k≤2011)[1\/(x-k)],所以,f'(x) =f(x)*∑(1≤k≤2011)[1\/(x-k)] = …….