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

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

$f\left(x\right) =$

$\left(2x-1\right){\cdot}{\mathrm{e}}^{2x}$

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

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

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

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

$=\class{steps-node}{\cssId{steps-node-9}{2}}{\cdot}\left(2x-1\right){\cdot}{\mathrm{e}}^{2x}+2{\mathrm{e}}^{2x}$