Find an equation of the tangent line to the graph of the fun

来源：学生作业帮编辑：搜狗做题网作业帮分类：数学作业时间：2024/06/17 02:08:48

Find an equation of the tangent line to the graph of the function f(x) = 8/(√x^2+3x) at the point (1,4)

题的意思是：求f(x)=8/√(x^2+3x)在点(1,4)处的切线方程
重点是求函数在x=1处的f'(x)
直接求导很麻烦,可采用对数求导法,
lnf(x)=ln8-(ln(x^2+3x))/2
两边同时对x求导,
f'(x)/f(x)=-(2x+3)/2(x^2+3x)
把x=1,f(x)=4带入,得
f'(x)=-5/2
可以求出切线方程为y-4=-5(x-1)/2
整理得2y+5y-13=0
再问： lnf(x)=ln8-(ln(x^2+3x))/2 为什麽要除以2？那如果用直接求导的话，我应该看得懂...
再答：因为分母是根号下那么多，具体写法是

直接求导非常麻烦，分母还有根号的一般采用这种对数求导法

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