Derieving Derivative #2
Calculus
Level
3
The function is a decreasing function in the interval
None of these
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1 solution
If f(x) = x^x, then ln(f) = x ln(x), (1/f) (df/dx) = x*(1/x) + ln(x) = 1 + ln(x), and df/dx = x^x(1 + ln(x) which is negative if 1 + ln(x) < 0 ,or ln(x) < -1, but ln(1/e) = ln(1) - ln(e) = -1, so interval is (0,1/e)