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

$f\left(x\right) =$	$\left(x-1\right){\cdot}\sqrt{{x}^{2}-1}$
$\dfrac{\mathrm{d}\left(f\left(x\right)\right)}{\mathrm{d}x} =$	$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\left(x-1\right){\cdot}\sqrt{{x}^{2}-1}\right)}}$ $=\class{steps-node}{\cssId{steps-node-3}{\class{steps-node}{\cssId{steps-node-2}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(x-1\right)}}{\cdot}\sqrt{{x}^{2}-1}}}+\class{steps-node}{\cssId{steps-node-5}{\left(x-1\right){\cdot}\class{steps-node}{\cssId{steps-node-4}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\sqrt{{x}^{2}-1}\right)}}}}$ $=\class{steps-node}{\cssId{steps-node-6}{1}}{\cdot}\sqrt{{x}^{2}-1}+\class{steps-node}{\cssId{steps-node-7}{\dfrac{1}{2{\cdot}\sqrt{{x}^{2}-1}}}}{\cdot}\class{steps-node}{\cssId{steps-node-8}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({x}^{2}-1\right)}}{\cdot}\left(x-1\right)$ $=\sqrt{{x}^{2}-1}+\dfrac{\class{steps-node}{\cssId{steps-node-9}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({x}^{2}\right)}}{\cdot}\left(x-1\right)}{2{\cdot}\sqrt{{x}^{2}-1}}$ $=\sqrt{{x}^{2}-1}+\dfrac{\class{steps-node}{\cssId{steps-node-10}{2}}\class{steps-node}{\cssId{steps-node-11}{x}}{\cdot}\left(x-1\right)}{2{\cdot}\sqrt{{x}^{2}-1}}$ $=\sqrt{{x}^{2}-1}+\dfrac{\left(x-1\right){\cdot}x}{\sqrt{{x}^{2}-1}}$

$f\left(x\right) =$

$\left(x-1\right){\cdot}\sqrt{{x}^{2}-1}$

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

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

$=\class{steps-node}{\cssId{steps-node-3}{\class{steps-node}{\cssId{steps-node-2}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(x-1\right)}}{\cdot}\sqrt{{x}^{2}-1}}}+\class{steps-node}{\cssId{steps-node-5}{\left(x-1\right){\cdot}\class{steps-node}{\cssId{steps-node-4}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\sqrt{{x}^{2}-1}\right)}}}}$

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

$=\sqrt{{x}^{2}-1}+\dfrac{\class{steps-node}{\cssId{steps-node-9}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({x}^{2}\right)}}{\cdot}\left(x-1\right)}{2{\cdot}\sqrt{{x}^{2}-1}}$

$=\sqrt{{x}^{2}-1}+\dfrac{\class{steps-node}{\cssId{steps-node-10}{2}}\class{steps-node}{\cssId{steps-node-11}{x}}{\cdot}\left(x-1\right)}{2{\cdot}\sqrt{{x}^{2}-1}}$

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