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Pochodna funkcji 6sqrt(3,x)-4sqrt(4,x)

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

$f\left(x\right) =$

$6{x}^{\frac{1}{3}}-4{x}^{\frac{1}{4}}$

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

$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(6{x}^{\frac{1}{3}}-4{x}^{\frac{1}{4}}\right)}}$

$=\class{steps-node}{\cssId{steps-node-2}{6{\cdot}\class{steps-node}{\cssId{steps-node-3}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({x}^{\frac{1}{3}}\right)}}-4{\cdot}\class{steps-node}{\cssId{steps-node-4}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({x}^{\frac{1}{4}}\right)}}}}$

$=6{\cdot}\class{steps-node}{\cssId{steps-node-5}{\dfrac{1}{3}}}{\cdot}\class{steps-node}{\cssId{steps-node-6}{{x}^{\frac{1}{3}-1}}}-4{\cdot}\class{steps-node}{\cssId{steps-node-7}{\dfrac{1}{4}}}{\cdot}\class{steps-node}{\cssId{steps-node-8}{{x}^{\frac{1}{4}-1}}}$

$=\dfrac{2}{{x}^{\frac{2}{3}}}-\dfrac{1}{{x}^{\frac{3}{4}}}$