close
標題:
如何微分e^x？
發問:
最佳解答:
Let y=ex ln y = x ln e ln y = x Differentiating both sides w.r.t. x (dy/dx)/y = 1 dy/dx = y dy/dx = ex
其他解答:
e^x is definated to have properties that d (e^x) /dx=e^x, so it is not calculated in this way. e^x is defined as e^x=1+x+x^2/2+x^3/3!+.... to infinity e^x = summation n=0 to infinity x^n/n! This defination will lead to that the dev. of e^x will be itself. The any term m of the summation after dev. is d (x^m/m!) /dx=mx^(m-1)/m!=x^(m-1)/(m-1)! so all the term added up will be: d(1+x+x^2/2+x^3/3!+.... +x^m/m!+.......)/dx =0+1+x+x^2/2+........+x^(m-1)/(m-1)!+...........=e^x It is a definated function. 2008-02-04 14:26:10 補充： e^x can be defined in other way.e^x=lim n trends infinity (1+x/n)^nYou can see d lim n trends infinity (1+x/n)^n / dx=lim n trends infinity n(1+x/n)^(n-1)(1/n)=lim n trends infinity (1+x/n)^(n-1)n is about same as n-1 for a very large n=lim n trends infinity (1+x/(n-1))^(n-1)=e^x
如何微分e^x？
發問:
此文章來自奇摩知識+如有不便請留言告知
我知道d/dx e^x=e^x 實際運算是怎樣？ 更新: very good!!!最佳解答:
Let y=ex ln y = x ln e ln y = x Differentiating both sides w.r.t. x (dy/dx)/y = 1 dy/dx = y dy/dx = ex
其他解答:
e^x is definated to have properties that d (e^x) /dx=e^x, so it is not calculated in this way. e^x is defined as e^x=1+x+x^2/2+x^3/3!+.... to infinity e^x = summation n=0 to infinity x^n/n! This defination will lead to that the dev. of e^x will be itself. The any term m of the summation after dev. is d (x^m/m!) /dx=mx^(m-1)/m!=x^(m-1)/(m-1)! so all the term added up will be: d(1+x+x^2/2+x^3/3!+.... +x^m/m!+.......)/dx =0+1+x+x^2/2+........+x^(m-1)/(m-1)!+...........=e^x It is a definated function. 2008-02-04 14:26:10 補充： e^x can be defined in other way.e^x=lim n trends infinity (1+x/n)^nYou can see d lim n trends infinity (1+x/n)^n / dx=lim n trends infinity n(1+x/n)^(n-1)(1/n)=lim n trends infinity (1+x/n)^(n-1)n is about same as n-1 for a very large n=lim n trends infinity (1+x/(n-1))^(n-1)=e^x
文章標籤
全站熱搜
留言列表
