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Pochodna funkcji x^2*sqrt(2,1-x)

$f\left(x\right) =$	$\sqrt{1-x}{\cdot}{x}^{2}$
$\dfrac{\mathrm{d}\left(f\left(x\right)\right)}{\mathrm{d}x} =$	$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\sqrt{1-x}{\cdot}{x}^{2}\right)}}$ $=\class{steps-node}{\cssId{steps-node-3}{\class{steps-node}{\cssId{steps-node-2}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\sqrt{1-x}\right)}}{\cdot}{x}^{2}}}+\class{steps-node}{\cssId{steps-node-5}{\sqrt{1-x}{\cdot}\class{steps-node}{\cssId{steps-node-4}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({x}^{2}\right)}}}}$ $=\class{steps-node}{\cssId{steps-node-6}{\dfrac{1}{2{\cdot}\sqrt{1-x}}}}{\cdot}\class{steps-node}{\cssId{steps-node-7}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(1-x\right)}}{\cdot}{x}^{2}+\class{steps-node}{\cssId{steps-node-8}{2}}\class{steps-node}{\cssId{steps-node-9}{x}}{\cdot}\sqrt{1-x}$ $=\dfrac{\class{steps-node}{\cssId{steps-node-10}{-1}}{x}^{2}}{2{\cdot}\sqrt{1-x}}+2{\cdot}\sqrt{1-x}{\cdot}x$ $=2{\cdot}\sqrt{1-x}{\cdot}x-\dfrac{{x}^{2}}{2{\cdot}\sqrt{1-x}}$

$f\left(x\right) =$

$\sqrt{1-x}{\cdot}{x}^{2}$

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

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

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

$=\class{steps-node}{\cssId{steps-node-6}{\dfrac{1}{2{\cdot}\sqrt{1-x}}}}{\cdot}\class{steps-node}{\cssId{steps-node-7}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(1-x\right)}}{\cdot}{x}^{2}+\class{steps-node}{\cssId{steps-node-8}{2}}\class{steps-node}{\cssId{steps-node-9}{x}}{\cdot}\sqrt{1-x}$

$=\dfrac{\class{steps-node}{\cssId{steps-node-10}{-1}}{x}^{2}}{2{\cdot}\sqrt{1-x}}+2{\cdot}\sqrt{1-x}{\cdot}x$

$=2{\cdot}\sqrt{1-x}{\cdot}x-\dfrac{{x}^{2}}{2{\cdot}\sqrt{1-x}}$