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Pochodna funkcji (1-x^2/2)^2

$f\left(x\right) =$	${\left(1-\dfrac{{x}^{2}}{2}\right)}^{2}$
$\dfrac{\mathrm{d}\left(f\left(x\right)\right)}{\mathrm{d}x} =$	$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({\left(1-\dfrac{{x}^{2}}{2}\right)}^{2}\right)}}$ $=\class{steps-node}{\cssId{steps-node-2}{2}}{\cdot}\class{steps-node}{\cssId{steps-node-3}{\left(1-\dfrac{{x}^{2}}{2}\right)}}{\cdot}\class{steps-node}{\cssId{steps-node-4}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(1-\dfrac{{x}^{2}}{2}\right)}}$ $=2{\cdot}\class{steps-node}{\cssId{steps-node-5}{\dfrac{-\class{steps-node}{\cssId{steps-node-6}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({x}^{2}\right)}}}{2}}}{\cdot}\left(1-\dfrac{{x}^{2}}{2}\right)$ $=-\left(\class{steps-node}{\cssId{steps-node-7}{2}}\class{steps-node}{\cssId{steps-node-8}{x}}\right){\cdot}\left(1-\dfrac{{x}^{2}}{2}\right)$ Uproszczony wynik: $=-2x{\cdot}\left(1-\dfrac{{x}^{2}}{2}\right)$

$f\left(x\right) =$

${\left(1-\dfrac{{x}^{2}}{2}\right)}^{2}$

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

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

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

$=2{\cdot}\class{steps-node}{\cssId{steps-node-5}{\dfrac{-\class{steps-node}{\cssId{steps-node-6}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({x}^{2}\right)}}}{2}}}{\cdot}\left(1-\dfrac{{x}^{2}}{2}\right)$

$=-\left(\class{steps-node}{\cssId{steps-node-7}{2}}\class{steps-node}{\cssId{steps-node-8}{x}}\right){\cdot}\left(1-\dfrac{{x}^{2}}{2}\right)$

Uproszczony wynik:

$=-2x{\cdot}\left(1-\dfrac{{x}^{2}}{2}\right)$