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Pochodna funkcji 2e^xctgx

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

$f\left(x\right) =$

$2cgtx{\cdot}{\mathrm{e}}^{x}$

Note: Your input has been rewritten/simplified.

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

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

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

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

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

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

Wynik alternatywny:

$=2cgtx{\cdot}{\mathrm{e}}^{x}+2cgt{\cdot}{\mathrm{e}}^{x}$