Q1) y=ln e^x
Q2) y=(e^-x) ln x
Q3) y=e^(x^2 ln x^2)
Q4) y=ln e^(4x+1)
please find dy/dx, give a step and a answer, thanks a lot
easy differentiation-回答送分
2009-10-14 7:14 pm
回答 (1)
2009-10-14 7:20 pm
✔ 最佳答案
1. y = lnexy = xlne (Property of logarithm)
y = x
dy/dx = dx/dx = 1
2. y = e-xlnx
dy/dx = e-x d(lnx)/dx + lnx d(e-x)/dx (Product rule)
dy/dx = e-x/x - e-xlnx
= e-x[(1/x) - lnx]
3. y = exp(x2lnx2)
dy/dx = d(exp(x2lnx2))/d(x2lnx2) d(x2lnx2)/dx (Chain rule)
= exp(x2lnx2) ((2x)x2 / x2) X 2xlnx2
= 4x2(lnx2)exp(x2lnx2)
4. y = lne4x+1
y = 4x + 1
dy/dx = d(4x + 1)/dx = 4
參考: Physics king
收錄日期: 2021-04-19 15:55:51
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