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Pochodna funkcji ln(sqrt(x+1)/(x-1))

$f\left(x\right) =$	$\dfrac{\ln\left(x+1\right)}{2}-\ln\left(x-1\right)$ Note: Your input has been rewritten/simplified.
$\dfrac{\mathrm{d}\left(f\left(x\right)\right)}{\mathrm{d}x} =$	$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\dfrac{\ln\left(x+1\right)}{2}-\ln\left(x-1\right)\right)}}$ $=\class{steps-node}{\cssId{steps-node-2}{\dfrac{\class{steps-node}{\cssId{steps-node-3}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\ln\left(x+1\right)\right)}}}{2}-\class{steps-node}{\cssId{steps-node-4}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\ln\left(x-1\right)\right)}}}}$ $=\dfrac{\class{steps-node}{\cssId{steps-node-5}{\dfrac{1}{x+1}}}{\cdot}\class{steps-node}{\cssId{steps-node-6}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(x+1\right)}}}{2}-\class{steps-node}{\cssId{steps-node-7}{\dfrac{1}{x-1}}}{\cdot}\class{steps-node}{\cssId{steps-node-8}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(x-1\right)}}$ $=\dfrac{\class{steps-node}{\cssId{steps-node-9}{1}}}{2{\cdot}\left(x+1\right)}-\dfrac{\class{steps-node}{\cssId{steps-node-10}{1}}}{x-1}$

$f\left(x\right) =$

$\dfrac{\ln\left(x+1\right)}{2}-\ln\left(x-1\right)$

Note: Your input has been rewritten/simplified.

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

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

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

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

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