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