Gehört zu den grundlegenden Ableitungen : merken
[ e^term ] ´ = e^term + ( term ´ )
e^{-0.5* (x-1)hoch2}
term = -0.5 * (x-1)^2
term ´ = -0.5 * 2 * ( x -1 ) * 1
term ´= -1 * ( x - 1 )
term ´ = 1 - x
[ e^term ] ´ = e^term + ( 1 - x )
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2. Ableitung : zusätzlich die Produktregel
( u * v ) ´ = u ´ * v + u * v ´
[ e^term + ( 1 - x ) ] ´
u = e^term
u ´ = e^term + ( 1 - x )
v = ( 1 - x )
v ´= -1
( u * v ) ´ = u ´ * v + u * v ´
[ e^term + ( 1 - x ) ] ´ = e^term ´ * ( 1 - x ) + e^term * ( -1 )
[ e^term + ( 1 - x ) ] ´ = ( e^term + ( 1 - x ) * ( 1 - x ) + e^term * ( -1 )
[ e^term + ( 1 - x ) ] ´ = e^term * ( 1 -2* x + x^2 + ( -1 ) )
[ e^term + ( 1 - x ) ] ´ = e^term * ( -2* x + x^2 )
[ e^term + ( 1 - x ) ] ´ = x * e^term * ( -2 + x )