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Pochodna funkcji xe^-2x

$f\left(x\right) =$	${\mathrm{e}}^{-2}{\cdot}{x}^{2}$
$\dfrac{\mathrm{d}\left(f\left(x\right)\right)}{\mathrm{d}x} =$	$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({\mathrm{e}}^{-2}{\cdot}{x}^{2}\right)}}$ $=\class{steps-node}{\cssId{steps-node-2}{{\mathrm{e}}^{-2}{\cdot}\class{steps-node}{\cssId{steps-node-3}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({x}^{2}\right)}}}}$ $={\mathrm{e}}^{-2}{\cdot}\class{steps-node}{\cssId{steps-node-4}{2}}\class{steps-node}{\cssId{steps-node-5}{x}}$ $=2{\mathrm{e}}^{-2}{\cdot}x$

$f\left(x\right) =$

${\mathrm{e}}^{-2}{\cdot}{x}^{2}$

$\dfrac{\mathrm{d}\left(f\left(x\right)\right)}{\mathrm{d}x} =$

$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({\mathrm{e}}^{-2}{\cdot}{x}^{2}\right)}}$

$=\class{steps-node}{\cssId{steps-node-2}{{\mathrm{e}}^{-2}{\cdot}\class{steps-node}{\cssId{steps-node-3}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({x}^{2}\right)}}}}$

$={\mathrm{e}}^{-2}{\cdot}\class{steps-node}{\cssId{steps-node-4}{2}}\class{steps-node}{\cssId{steps-node-5}{x}}$

$=2{\mathrm{e}}^{-2}{\cdot}x$