Consider a function...?
回答 (2)
2020-09-16 12:44 am
Use logarithmic differentiation
Take ln of both sides --> ln(h) = ln(x^f) =f*ln(x)
differentiate wrt x --> 1/h dh/dx = f/x + ln(x) df/dx
dh/dx = {f/x + ln(x) df/dx}h = {f/x + ln(x) df/dx}*x^f
set x = e --> dh/dx|x=e = {f(e)/e +ln(e) df/dx|x=e} e^f(e)
= {5/e + 7}e^5 = (5 +7e)e^4
Take ln of both sides --> ln(h) = ln(x^f) =f*ln(x)
differentiate wrt x --> 1/h dh/dx = f/x + ln(x) df/dx
dh/dx = {f/x + ln(x) df/dx}h = {f/x + ln(x) df/dx}*x^f
set x = e --> dh/dx|x=e = {f(e)/e +ln(e) df/dx|x=e} e^f(e)
= {5/e + 7}e^5 = (5 +7e)e^4
收錄日期: 2021-04-24 08:02:13
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20200915162314AAVfUfq