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Pochodna funkcji 2xe^(-x^2/4)

$f\left(x\right) =$	$2x{\cdot}{\mathrm{e}}^{-\frac{{x}^{2}}{4}}$ Note: Your input has been rewritten/simplified.
$\dfrac{\mathrm{d}\left(f\left(x\right)\right)}{\mathrm{d}x} =$	$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(2x{\cdot}{\mathrm{e}}^{-\frac{{x}^{2}}{4}}\right)}}$ $=\class{steps-node}{\cssId{steps-node-2}{2{\cdot}\class{steps-node}{\cssId{steps-node-3}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(x{\cdot}{\mathrm{e}}^{-\frac{{x}^{2}}{4}}\right)}}}}$ $=2{\cdot}\left(\class{steps-node}{\cssId{steps-node-5}{\class{steps-node}{\cssId{steps-node-4}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(x\right)}}{\cdot}{\mathrm{e}}^{-\frac{{x}^{2}}{4}}}}+\class{steps-node}{\cssId{steps-node-7}{x{\cdot}\class{steps-node}{\cssId{steps-node-6}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({\mathrm{e}}^{-\frac{{x}^{2}}{4}}\right)}}}}\right)$ $=2{\cdot}\left(\class{steps-node}{\cssId{steps-node-8}{1}}{\mathrm{e}}^{-\frac{{x}^{2}}{4}}+\class{steps-node}{\cssId{steps-node-9}{{\mathrm{e}}^{-\frac{{x}^{2}}{4}}}}{\cdot}\class{steps-node}{\cssId{steps-node-10}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(-\dfrac{{x}^{2}}{4}\right)}}{\cdot}x\right)$ $=2{\cdot}\left(\class{steps-node}{\cssId{steps-node-11}{\dfrac{-\class{steps-node}{\cssId{steps-node-12}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({x}^{2}\right)}}}{4}}}{\cdot}x{\cdot}{\mathrm{e}}^{-\frac{{x}^{2}}{4}}+{\mathrm{e}}^{-\frac{{x}^{2}}{4}}\right)$ $=2{\cdot}\left({\mathrm{e}}^{-\frac{{x}^{2}}{4}}-\dfrac{\class{steps-node}{\cssId{steps-node-13}{2}}\class{steps-node}{\cssId{steps-node-14}{x}}{\cdot}x{\cdot}{\mathrm{e}}^{-\frac{{x}^{2}}{4}}}{4}\right)$ $=2{\cdot}\left({\mathrm{e}}^{-\frac{{x}^{2}}{4}}-\dfrac{{x}^{2}{\cdot}{\mathrm{e}}^{-\frac{{x}^{2}}{4}}}{2}\right)$ Uproszczony wynik: $=2{\mathrm{e}}^{-\frac{{x}^{2}}{4}}-{x}^{2}{\cdot}{\mathrm{e}}^{-\frac{{x}^{2}}{4}}$

$f\left(x\right) =$

$2x{\cdot}{\mathrm{e}}^{-\frac{{x}^{2}}{4}}$

Note: Your input has been rewritten/simplified.

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

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

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

$=2{\cdot}\left(\class{steps-node}{\cssId{steps-node-5}{\class{steps-node}{\cssId{steps-node-4}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(x\right)}}{\cdot}{\mathrm{e}}^{-\frac{{x}^{2}}{4}}}}+\class{steps-node}{\cssId{steps-node-7}{x{\cdot}\class{steps-node}{\cssId{steps-node-6}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({\mathrm{e}}^{-\frac{{x}^{2}}{4}}\right)}}}}\right)$

$=2{\cdot}\left(\class{steps-node}{\cssId{steps-node-8}{1}}{\mathrm{e}}^{-\frac{{x}^{2}}{4}}+\class{steps-node}{\cssId{steps-node-9}{{\mathrm{e}}^{-\frac{{x}^{2}}{4}}}}{\cdot}\class{steps-node}{\cssId{steps-node-10}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(-\dfrac{{x}^{2}}{4}\right)}}{\cdot}x\right)$

$=2{\cdot}\left(\class{steps-node}{\cssId{steps-node-11}{\dfrac{-\class{steps-node}{\cssId{steps-node-12}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({x}^{2}\right)}}}{4}}}{\cdot}x{\cdot}{\mathrm{e}}^{-\frac{{x}^{2}}{4}}+{\mathrm{e}}^{-\frac{{x}^{2}}{4}}\right)$

$=2{\cdot}\left({\mathrm{e}}^{-\frac{{x}^{2}}{4}}-\dfrac{\class{steps-node}{\cssId{steps-node-13}{2}}\class{steps-node}{\cssId{steps-node-14}{x}}{\cdot}x{\cdot}{\mathrm{e}}^{-\frac{{x}^{2}}{4}}}{4}\right)$

$=2{\cdot}\left({\mathrm{e}}^{-\frac{{x}^{2}}{4}}-\dfrac{{x}^{2}{\cdot}{\mathrm{e}}^{-\frac{{x}^{2}}{4}}}{2}\right)$

Uproszczony wynik:

$=2{\mathrm{e}}^{-\frac{{x}^{2}}{4}}-{x}^{2}{\cdot}{\mathrm{e}}^{-\frac{{x}^{2}}{4}}$