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

$f\left(x\right) =$	$\dfrac{-2x}{x-1}$
$\dfrac{\mathrm{d}\left(f\left(x\right)\right)}{\mathrm{d}x} =$	$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\dfrac{-2x}{x-1}\right)}}$ $=\class{steps-node}{\cssId{steps-node-2}{-2{\cdot}\class{steps-node}{\cssId{steps-node-3}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\dfrac{x}{x-1}\right)}}}}$ $=-2{\cdot}\dfrac{\class{steps-node}{\cssId{steps-node-6}{\left(x-1\right){\cdot}\class{steps-node}{\cssId{steps-node-5}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(x\right)}}}}-\class{steps-node}{\cssId{steps-node-8}{\class{steps-node}{\cssId{steps-node-7}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(x-1\right)}}{\cdot}x}}}{\class{steps-node}{\cssId{steps-node-4}{{\left(x-1\right)}^{2}}}}$ $=\dfrac{-2{\cdot}\left(\class{steps-node}{\cssId{steps-node-9}{1}}{\cdot}\left(x-1\right)-\class{steps-node}{\cssId{steps-node-10}{1}}x\right)}{{\left(x-1\right)}^{2}}$ $=\dfrac{2}{{\left(x-1\right)}^{2}}$ Wynik alternatywny: $=\dfrac{2x}{{\left(x-1\right)}^{2}}-\dfrac{2}{x-1}$

$f\left(x\right) =$

$\dfrac{-2x}{x-1}$

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

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

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

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

$=\dfrac{-2{\cdot}\left(\class{steps-node}{\cssId{steps-node-9}{1}}{\cdot}\left(x-1\right)-\class{steps-node}{\cssId{steps-node-10}{1}}x\right)}{{\left(x-1\right)}^{2}}$

$=\dfrac{2}{{\left(x-1\right)}^{2}}$

Wynik alternatywny:

$=\dfrac{2x}{{\left(x-1\right)}^{2}}-\dfrac{2}{x-1}$