1.F'(X)
2 F"(X)
3 range of graph
更新1:
how about in negative range of X there is unresonable change of value and dy/dx ,and the concave problem
curve of x^x=y
回答 (2)
2011-07-11 10:27 pm
✔ 最佳答案
y = x^x1. ln y = ln (x^x)
= x (ln x)
Differentiating on both sides with respect to x, we have
1/y dy/dx = (ln x) dx/dx + x d(ln x)/dx
= ln x + x * 1/x
= ln x + 1
dy/dx = (ln x + 1)y
f'(x)= (ln x + 1)(x^x)
2. f"(x) = (ln x + 1) d(x^x)/dx + (x^x) d(ln x + 1)/dx
= (ln x + 1) [(ln x + 1)(x^x)] + (x^x)(1/x)
= x^x (ln x + 1)^2 + (x^x)(1/x)
= (x^x) [(ln x + 1)^2 + 1/x]
2011-07-08 4:53 am
y = x^x
1. ln y = ln (x^x)
= x (ln x)
Differentiating on both sides with respect to x, we have
1/y dy/dx = (ln x) dx/dx + x d(ln x)/dx
= ln x + x * 1/x
= ln x + 1
dy/dx = (ln x + 1)y
f'(x)= (ln x + 1)(x^x)
2. f"(x) = (ln x + 1) d(x^x)/dx + (x^x) d(ln x + 1)/dx
= (ln x + 1) [(ln x + 1)(x^x)] + (x^x)(1/x)
= x^x (ln x + 1)^2 + (x^x)(1/x)
= (x^x) [(ln x + 1)^2 + 1/x]
3. Because 0^0 is undefined, x is undefined when x = 0
The range of graph is all real values of x except 0
1. ln y = ln (x^x)
= x (ln x)
Differentiating on both sides with respect to x, we have
1/y dy/dx = (ln x) dx/dx + x d(ln x)/dx
= ln x + x * 1/x
= ln x + 1
dy/dx = (ln x + 1)y
f'(x)= (ln x + 1)(x^x)
2. f"(x) = (ln x + 1) d(x^x)/dx + (x^x) d(ln x + 1)/dx
= (ln x + 1) [(ln x + 1)(x^x)] + (x^x)(1/x)
= x^x (ln x + 1)^2 + (x^x)(1/x)
= (x^x) [(ln x + 1)^2 + 1/x]
3. Because 0^0 is undefined, x is undefined when x = 0
The range of graph is all real values of x except 0
收錄日期: 2021-04-23 21:06:12
原文連結 [永久失效]:
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