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Pochodna funkcji arctan(sqrt(x*x-1))

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

$f\left(x\right) =$

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

Note: Your input has been rewritten/simplified.

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

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

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

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

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

$=\dfrac{\class{steps-node}{\cssId{steps-node-7}{2}}\class{steps-node}{\cssId{steps-node-8}{x}}}{2{x}^{2}{\cdot}\sqrt{{x}^{2}-1}}$

$=\dfrac{1}{x{\cdot}\sqrt{{x}^{2}-1}}$