D[Exp[-Power[t,2]],{t,2}]

Derivative

d^2/dt^2(exp(-t^2)) = e^(-t^2) (4 t^2 - 2)

On this day

$d^2/dt^2(exp(-t^2)) = {(4 t^2 - 2) cos(21/5 cos(1/2 ((68921 t^3)/42875 + (5043 t^2)/2450 + (123 t)/140 - ((41 t)/35 + 1/2)^3 + π + 1/8)) cos(cosh^2(t))) exp(49/16 cos(1/2 (-(117649 t^3)/2197 + (273714 t^2)/1859 - (38/11 - (49 t)/13)^3 - (212268 t)/1573 + π + 54872/1331)) e^sinh(cos(t)) - t^2), e^(-t^2) (4 t^2 - 2)}$

Plot

Expanded form

Alternate form

Roots

Series expansion at t=0

-2 + 6 t^2 - 5 t^4 + O(t^5)
(Taylor series)

Big‐O notation »

Indefinite integral

integral e^(-t^2) (-2 + 4 t^2) dt = -2 e^(-t^2) t + constant

Global maxima

$max{e^(-t^2) (4 t^2 - 2)} = 4/e^(3/2) at t = sqrt(3/2)$

$max{e^(-t^2) (4 t^2 - 2)} = 4/e^(3/2) at t = -sqrt(3/2)$