Differentiation

Angel15

2010-03-21 8:13 am

Differentiate each of the functions with respect to x.
1.y= 4/(e^x+e^-x)

2.y=(1+e^-x)/(1-e^-x)

3.y=(e^x+e^-x)/(1+e^-2x)

4.y=(e^x)/(((e^x)+1)^0.5)

Given that f(x) is a differentiable function, f(2)=0 and f '(2)=3. Find the values of the derivatives at each of the following given values of x.

If G(x)=(x-f(x)/((e^f(x))+1)^0.5 , find G '(2)

And plz explain under what condition I should use 'Chain Rule' briefly.

回答 (1)

hung

2010-03-21 7:22 pm

✔ 最佳答案

http://www.dumpt.com/img/viewer.php?file=tq945n6d9wvf6n3z3sc5.bmp
答題在那個網址上。

chain rule 基本是是經常用的 , 當題目要求你respect with x 咁"d" , 但係個函數入面並非x , eg 第1題的 e^(-x)

當我地用chain rule 實際上是將 respect with x 變成 respect with -x , 將補返d野係後面

即係 d(e^ -x) / dx = d(e^ -x) / d(-x) 乘 d(-x) / dx 咁e入面果舊就同respect with 果舊一樣先用公式 ( d(e^y) / dy = e^y )

2010-03-21 11:23:18 補充：
第三段 : 當我地用chain rule .... respect with x 變成 respect with -x 只係for 例子 e^(-x)

參考: myself

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