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Pochodna funkcji e^-x^2

$f\left(x\right) =$	${\mathrm{e}}^{-{x}^{2}}$
$\dfrac{\mathrm{d}\left(f\left(x\right)\right)}{\mathrm{d}x} =$	$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({\mathrm{e}}^{-{x}^{2}}\right)}}$ $=\class{steps-node}{\cssId{steps-node-2}{{\mathrm{e}}^{-{x}^{2}}}}{\cdot}\class{steps-node}{\cssId{steps-node-3}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(-{x}^{2}\right)}}$ $=\class{steps-node}{\cssId{steps-node-4}{-\class{steps-node}{\cssId{steps-node-5}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({x}^{2}\right)}}}}{\cdot}{\mathrm{e}}^{-{x}^{2}}$ $=-\left(\class{steps-node}{\cssId{steps-node-6}{2}}\class{steps-node}{\cssId{steps-node-7}{x}}\right){\cdot}{\mathrm{e}}^{-{x}^{2}}$ Uproszczony wynik: $=-2x{\cdot}{\mathrm{e}}^{-{x}^{2}}$

$f\left(x\right) =$

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

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

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

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

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

$=-\left(\class{steps-node}{\cssId{steps-node-6}{2}}\class{steps-node}{\cssId{steps-node-7}{x}}\right){\cdot}{\mathrm{e}}^{-{x}^{2}}$

Uproszczony wynik:

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