試求下列各函數之導函數：f(x)=(√x +x^2) / x
老師教我的算法如下
原試=[(√x)/x]+(x^2/x)=[(x^1/2)/x]+x=[x^(1/2)-1]+x
到這邊我就不知道怎麼算了，希望各位大大教教我
答案是(-1/2√x^3)+1
有一題高二數學微分公式的題目不會(希望各位大大幫幫我
2015-05-10 12:05 am
回答 (2)
2015-05-10 12:28 am
2015-05-12 10:51 am
f(x) = (√x +x^2)/x = (x^{1/2}+x^2)/x = x^{1/2}/x + x^2/x
= x^{1/2-1} + x^{2-1} = x^{-1/2} + x
所以
f'(x) = (-1/2)x^{-1/2-1}+1 = (-1/2)x^{-3/2} + 1 = (-1/2)/√x^3 + 1
= x^{1/2-1} + x^{2-1} = x^{-1/2} + x
所以
f'(x) = (-1/2)x^{-1/2-1}+1 = (-1/2)x^{-3/2} + 1 = (-1/2)/√x^3 + 1
收錄日期: 2021-05-04 01:57:29
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20150509000015KK03535