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 |