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

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

$f\left(x\right) =$

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

Note: Your input has been rewritten/simplified.

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

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

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

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

$=\dfrac{\dfrac{\class{steps-node}{\cssId{steps-node-9}{1}}}{x+1}-\dfrac{\class{steps-node}{\cssId{steps-node-10}{1}}}{x-1}}{2}$