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Pochodna funkcji (2(x^2)^(1/3)-x)(4(x^4)^(1/3)+2(x^5)^(1/3)+x^2)

$f\left(x\right) =$	$\left(2{x}^{\frac{2}{3}}-x\right){\cdot}\left({x}^{2}+2{x}^{\frac{5}{3}}+4{x}^{\frac{4}{3}}\right)$ Note: Your input has been rewritten/simplified.
$\dfrac{\mathrm{d}\left(f\left(x\right)\right)}{\mathrm{d}x} =$	$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\left(2{x}^{\frac{2}{3}}-x\right){\cdot}\left({x}^{2}+2{x}^{\frac{5}{3}}+4{x}^{\frac{4}{3}}\right)\right)}}$ $=\class{steps-node}{\cssId{steps-node-3}{\class{steps-node}{\cssId{steps-node-2}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(2{x}^{\frac{2}{3}}-x\right)}}{\cdot}\left({x}^{2}+2{x}^{\frac{5}{3}}+4{x}^{\frac{4}{3}}\right)}}+\class{steps-node}{\cssId{steps-node-5}{\left(2{x}^{\frac{2}{3}}-x\right){\cdot}\class{steps-node}{\cssId{steps-node-4}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({x}^{2}+2{x}^{\frac{5}{3}}+4{x}^{\frac{4}{3}}\right)}}}}$ $=\class{steps-node}{\cssId{steps-node-6}{\left(2{\cdot}\class{steps-node}{\cssId{steps-node-7}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({x}^{\frac{2}{3}}\right)}}-1\right)}}{\cdot}\left({x}^{2}+2{x}^{\frac{5}{3}}+4{x}^{\frac{4}{3}}\right)+\class{steps-node}{\cssId{steps-node-8}{\left(\class{steps-node}{\cssId{steps-node-9}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({x}^{2}\right)}}+2{\cdot}\class{steps-node}{\cssId{steps-node-10}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({x}^{\frac{5}{3}}\right)}}+4{\cdot}\class{steps-node}{\cssId{steps-node-11}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({x}^{\frac{4}{3}}\right)}}\right)}}{\cdot}\left(2{x}^{\frac{2}{3}}-x\right)$ $=\left(2{\cdot}\class{steps-node}{\cssId{steps-node-12}{\dfrac{2}{3}}}{\cdot}\class{steps-node}{\cssId{steps-node-13}{{x}^{\frac{2}{3}-1}}}-1\right){\cdot}\left({x}^{2}+2{x}^{\frac{5}{3}}+4{x}^{\frac{4}{3}}\right)+\left(4{\cdot}\class{steps-node}{\cssId{steps-node-18}{\dfrac{4}{3}}}{\cdot}\class{steps-node}{\cssId{steps-node-19}{{x}^{\frac{4}{3}-1}}}+2{\cdot}\class{steps-node}{\cssId{steps-node-16}{\dfrac{5}{3}}}{\cdot}\class{steps-node}{\cssId{steps-node-17}{{x}^{\frac{5}{3}-1}}}+\class{steps-node}{\cssId{steps-node-14}{2}}\class{steps-node}{\cssId{steps-node-15}{x}}\right){\cdot}\left(2{x}^{\frac{2}{3}}-x\right)$ $=\left(\dfrac{4}{3{x}^{\frac{1}{3}}}-1\right){\cdot}\left({x}^{2}+2{x}^{\frac{5}{3}}+4{x}^{\frac{4}{3}}\right)+\left(2{x}^{\frac{2}{3}}-x\right){\cdot}\left(2x+\dfrac{10{x}^{\frac{2}{3}}}{3}+\dfrac{16{x}^{\frac{1}{3}}}{3}\right)$

$f\left(x\right) =$

$\left(2{x}^{\frac{2}{3}}-x\right){\cdot}\left({x}^{2}+2{x}^{\frac{5}{3}}+4{x}^{\frac{4}{3}}\right)$

Note: Your input has been rewritten/simplified.

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

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

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

$=\class{steps-node}{\cssId{steps-node-6}{\left(2{\cdot}\class{steps-node}{\cssId{steps-node-7}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({x}^{\frac{2}{3}}\right)}}-1\right)}}{\cdot}\left({x}^{2}+2{x}^{\frac{5}{3}}+4{x}^{\frac{4}{3}}\right)+\class{steps-node}{\cssId{steps-node-8}{\left(\class{steps-node}{\cssId{steps-node-9}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({x}^{2}\right)}}+2{\cdot}\class{steps-node}{\cssId{steps-node-10}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({x}^{\frac{5}{3}}\right)}}+4{\cdot}\class{steps-node}{\cssId{steps-node-11}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({x}^{\frac{4}{3}}\right)}}\right)}}{\cdot}\left(2{x}^{\frac{2}{3}}-x\right)$

$=\left(2{\cdot}\class{steps-node}{\cssId{steps-node-12}{\dfrac{2}{3}}}{\cdot}\class{steps-node}{\cssId{steps-node-13}{{x}^{\frac{2}{3}-1}}}-1\right){\cdot}\left({x}^{2}+2{x}^{\frac{5}{3}}+4{x}^{\frac{4}{3}}\right)+\left(4{\cdot}\class{steps-node}{\cssId{steps-node-18}{\dfrac{4}{3}}}{\cdot}\class{steps-node}{\cssId{steps-node-19}{{x}^{\frac{4}{3}-1}}}+2{\cdot}\class{steps-node}{\cssId{steps-node-16}{\dfrac{5}{3}}}{\cdot}\class{steps-node}{\cssId{steps-node-17}{{x}^{\frac{5}{3}-1}}}+\class{steps-node}{\cssId{steps-node-14}{2}}\class{steps-node}{\cssId{steps-node-15}{x}}\right){\cdot}\left(2{x}^{\frac{2}{3}}-x\right)$

$=\left(\dfrac{4}{3{x}^{\frac{1}{3}}}-1\right){\cdot}\left({x}^{2}+2{x}^{\frac{5}{3}}+4{x}^{\frac{4}{3}}\right)+\left(2{x}^{\frac{2}{3}}-x\right){\cdot}\left(2x+\dfrac{10{x}^{\frac{2}{3}}}{3}+\dfrac{16{x}^{\frac{1}{3}}}{3}\right)$