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

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

$f\left(x\right) =$

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

Note: Your input has been rewritten/simplified.

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

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

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

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

$={\mathrm{e}}^{2}{\cdot}\left(\class{steps-node}{\cssId{steps-node-8}{1}}{\cdot}\left(2x-1\right)+\class{steps-node}{\cssId{steps-node-9}{2}}x\right)$

$={\mathrm{e}}^{2}{\cdot}\left(4x-1\right)$

Wynik alternatywny:

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