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Pochodna funkcji x^4+4sqrt(x)+1/x^4

$f\left(x\right) =$	${x}^{4}+4{\cdot}\sqrt{x}+\dfrac{1}{{x}^{4}}$
$\dfrac{\mathrm{d}\left(f\left(x\right)\right)}{\mathrm{d}x} =$	$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({x}^{4}+4{\cdot}\sqrt{x}+\dfrac{1}{{x}^{4}}\right)}}$ $=\class{steps-node}{\cssId{steps-node-2}{\class{steps-node}{\cssId{steps-node-3}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({x}^{4}\right)}}+4{\cdot}\class{steps-node}{\cssId{steps-node-4}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\sqrt{x}\right)}}+\class{steps-node}{\cssId{steps-node-5}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\dfrac{1}{{x}^{4}}\right)}}}}$ $=\dfrac{\class{steps-node}{\cssId{steps-node-11}{-\class{steps-node}{\cssId{steps-node-10}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({x}^{4}\right)}}}}}{\class{steps-node}{\cssId{steps-node-9}{{\left({x}^{4}\right)}^{2}}}}+4{\cdot}\class{steps-node}{\cssId{steps-node-8}{\dfrac{1}{2{\cdot}\sqrt{x}}}}+\class{steps-node}{\cssId{steps-node-6}{4}}\class{steps-node}{\cssId{steps-node-7}{{x}^{3}}}$ $=4{x}^{3}+\dfrac{2}{\sqrt{x}}-\dfrac{\class{steps-node}{\cssId{steps-node-12}{4}}\class{steps-node}{\cssId{steps-node-13}{{x}^{3}}}}{{x}^{8}}$ $=4{x}^{3}+\dfrac{2}{\sqrt{x}}-\dfrac{4}{{x}^{5}}$

$f\left(x\right) =$

${x}^{4}+4{\cdot}\sqrt{x}+\dfrac{1}{{x}^{4}}$

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

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

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

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

$=4{x}^{3}+\dfrac{2}{\sqrt{x}}-\dfrac{\class{steps-node}{\cssId{steps-node-12}{4}}\class{steps-node}{\cssId{steps-node-13}{{x}^{3}}}}{{x}^{8}}$

$=4{x}^{3}+\dfrac{2}{\sqrt{x}}-\dfrac{4}{{x}^{5}}$