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Pochodna funkcji 4/x^3

$f\left(x\right) =$	$\dfrac{4}{{x}^{3}}$
$\dfrac{\mathrm{d}\left(f\left(x\right)\right)}{\mathrm{d}x} =$	$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathbf{d}}{\mathbf{d}\boldsymbol{x}}\kern-.25em\left(\dfrac{4}{{x}^{3}}\right)}}$ $=\class{steps-node}{\cssId{steps-node-2}{4{\cdot}\class{steps-node}{\cssId{steps-node-3}{\tfrac{\mathbf{d}}{\mathbf{d}\boldsymbol{x}}\kern-.25em\left(\dfrac{1}{{x}^{3}}\right)}}}}$ $=4{\cdot}\dfrac{\class{steps-node}{\cssId{steps-node-6}{-\class{steps-node}{\cssId{steps-node-5}{\tfrac{\mathbf{d}}{\mathbf{d}\boldsymbol{x}}\kern-.25em\left({x}^{3}\right)}}}}}{\class{steps-node}{\cssId{steps-node-4}{{\left({x}^{3}\right)}^{2}}}}$ $=\dfrac{-4{\cdot}\class{steps-node}{\cssId{steps-node-7}{3}}\class{steps-node}{\cssId{steps-node-8}{{x}^{2}}}}{{x}^{6}}$ $=\dfrac{-12}{{x}^{4}}$

$f\left(x\right) =$

$\dfrac{4}{{x}^{3}}$

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

$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathbf{d}}{\mathbf{d}\boldsymbol{x}}\kern-.25em\left(\dfrac{4}{{x}^{3}}\right)}}$

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

$=4{\cdot}\dfrac{\class{steps-node}{\cssId{steps-node-6}{-\class{steps-node}{\cssId{steps-node-5}{\tfrac{\mathbf{d}}{\mathbf{d}\boldsymbol{x}}\kern-.25em\left({x}^{3}\right)}}}}}{\class{steps-node}{\cssId{steps-node-4}{{\left({x}^{3}\right)}^{2}}}}$

$=\dfrac{-4{\cdot}\class{steps-node}{\cssId{steps-node-7}{3}}\class{steps-node}{\cssId{steps-node-8}{{x}^{2}}}}{{x}^{6}}$

$=\dfrac{-12}{{x}^{4}}$