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Pochodna funkcji 1/x

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

$f\left(x\right) =$

$\dfrac{1}{x}$

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

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

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

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