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Pochodna funkcji x^2lnx

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

$f\left(x\right) =$

${x}^{2}{\cdot}\ln\left(x\right)$

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

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

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

$=\class{steps-node}{\cssId{steps-node-6}{2}}\class{steps-node}{\cssId{steps-node-7}{x}}{\cdot}\ln\left(x\right)+\class{steps-node}{\cssId{steps-node-8}{\dfrac{1}{x}}}{\cdot}{x}^{2}$

$=2x{\cdot}\ln\left(x\right)+x$