Derivative 4e^x
| Derivative |
|---|
| d/dx(4 e^x) = 4 e^x |
| Roots |
| (no roots exist) |
| Periodicity |
| periodic in x with period 2 i pi |
| Series expansion at x=0 |
| 4 + 4 x + 2 x^2 + (2 x^3)/3 + x^4/6 + O(x^5) (Taylor series) |
| Indefinite integral |
| integral 4 e^x dx = 4 e^x + constant |
| Limit |
| lim_(x->-infinity) 4 e^x = 0 |
| Definite integral |
| integral_(-infinity)^0 4 e^x dx = 4 |
| Definite integral over a half-period |
| integral_0^(i pi) 4 e^x dx = -8 |