what is the derivative of
[sin(x)]^x
更新1:
plz show me the process, thx
math problem derivative
2007-08-06 7:58 pm
i don't know how to do this problem, plz help!!!
what is the derivative of
[sin(x)]^x
what is the derivative of
[sin(x)]^x
回答 (2)
2007-08-07 8:02 am
✔ 最佳答案
By logarithm differentiation,let y=[sin(x)]^x,
then ln y = x ln sin(x)
differentiating both sides,
1/y(dy/dx) = ln sin(x) + x[1/sin(x)]cos(x)
dy/dx = [ln sin(x) + x(cos(x)/sin(x)]y
dy/dx = [ln sin(x) + xcot(x)][sin(x)]^x
2007-08-06 10:50 pm
d/dx ((sinx)^x)
=(d/d(sinx))((sinx)^x) * d/dx(sinx)
=(x(sinx))^(x-1) * cosx
=xcosx(sinx)^(x-1)
=(d/d(sinx))((sinx)^x) * d/dx(sinx)
=(x(sinx))^(x-1) * cosx
=xcosx(sinx)^(x-1)
參考: myself
收錄日期: 2021-05-03 11:49:28
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20070806000051KK01530