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Pochodna funkcji sqrt(x*x+1)

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

$f\left(x\right) =$

$\sqrt{{x}^{2}+1}$

Note: Your input has been rewritten/simplified.

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

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

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

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

$=\dfrac{\class{steps-node}{\cssId{steps-node-5}{2}}\class{steps-node}{\cssId{steps-node-6}{x}}}{2{\cdot}\sqrt{{x}^{2}+1}}$

$=\dfrac{x}{\sqrt{{x}^{2}+1}}$