Stemmer det

:D:D
[tex]f\left( x \right) = 2{x^2}{e^{ - x/2}} [/tex]
[tex] \left( {uv} \right) ^{\tiny\prime} = u ^{\tiny\prime}v + uv ^{\tiny\prime} [/tex]
[tex] u = 2{x^2},u ^{\tiny\prime} = 4x{\rm{ }}og{\rm{ }}v = {e^{ - x/2}},v ^{\tiny\prime} = - \frac{1}{2}{e^{ - x/2}} [/tex]
[tex] f\left( x \right) = 2{x^2}{e^{ - x/2}} [/tex]
[tex] f ^{\tiny\prime}\left( x \right) = \left( {4x} \right)\left( {{e^{ - x/2}}} \right) + \left( {2{x^2}} \right)\left( { - \frac{1}{2}{e^{ - x/2}}} \right) [/tex]
[tex] f ^{\tiny\prime}\left( x \right) = 4x \cdot {e^{ - x/2}} - {x^2} \cdot {e^{ - x/2}} [/tex]
[tex] f ^{\tiny\prime}\left( x \right) = x\left( {4 \cdot {e^{ - x/2}} - x \cdot {e^{ - x/2}}} \right) [/tex]
[tex] f ^{\tiny\prime}\left( x \right) = x\left( {4 - x} \right){e^{ - x/2}} [/tex]
[tex] f ^{\tiny\prime}\left( x \right) = - x\left( { - 4 + x} \right){e^{ - x/2}} [/tex]
[tex] \underline{\underline {f ^{\tiny\prime}\left( x \right) = - x\left( {x - 4} \right){e^{ - x/2}}}} [/tex]