Derivative 4e^x

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

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