how to use logarithmic differentiation to differentiate the following:
1. y=x^x
2. y=7^x
3. y=x^2x
4. y=sinx x 2^x
logarithmic differentiation
2012-04-28 8:04 pm
回答 (1)
2012-04-28 10:02 pm
✔ 最佳答案
1. ln y = x ln x1/y * dy/dx = x*1/x + ln x
dy/dx = x^x (1 + ln x)
2. ln y = x ln 7
1/y * dy/dx = ln 7
dy/dx = 7^x ln 7
3. ln y = 2x ln x
1/y * dy/dx = 2(x*1/x + ln x)
dy/dx = 2x^(2x) (1 + ln x)
4. ln y = ln(sin x) + ln (2^x)
= ln(sin x) + x ln 2
1/y * dy/dx = 1/sinx * cosx + ln 2
dy/dx = (2^x sin x)(cotx + ln 2)
參考: Knowledge is power.
收錄日期: 2021-04-23 18:33:53
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