I'm trying to derivate this function using the definition of derivate: x-sqrt(x).
I've reach this point:
(-(sqrt(x+h))+sqrt(x)+h)/h
I don't know what else to do, I'm stuck.
Help with derivate using definition?
回答 (1)
2015-09-26 5:28 am
✔ 最佳答案
as h→0( - √(x+h) + √x + h ) / h
→ 1 + (1/h)*[ √x - √(x+h) ]
( please note that h→0 , so h ≠ 0 , and hence h/h = 1 )
= 1 + (1/h)*[ √x - √(x+h) ]*[ √x + √(x+h) ]/[ √x + √(x+h) ]
= 1 + (1/h)*[ x - (x+h) ]/[ √x + √(x+h) ]
= 1 + (1/h)*( - h )/[ √x + √(x+h) ]
→ 1 - 1/[ √x + √(x+h) ]
→ 1 - 1/( √x + √x )
= 1 - 1/(2√x) ..... Ans
收錄日期: 2021-05-02 14:10:28
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20150924202434AAVEAwL