Derivative of ln(1+x)

Derivative of ln(1+x)

Derivative
d/dx(log(1 + x)) = 1/(x + 1)
Roots
(no roots exist)
Series expansion at x=0
1 – x + x^2 – x^3 + x^4 + O(x^5)
(Taylor series)
Series expansion at x=∞
1/x – (1/x)^2 + (1/x)^3 – (1/x)^4 + O((1/x)^5)
(Laurent series)
Indefinite integral
integral 1/(1 + x) dx = log(x + 1) + constant
Limit
lim_(x-> ± infinity) 1/(1 + x) = 0

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