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

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

$f\left(x\right) =$

${x}^{4}+{x}^{\frac{1}{4}}+\dfrac{1}{{x}^{4}}$

Note: Your input has been rewritten/simplified.

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

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

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

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

$=4{x}^{3}+\dfrac{1}{4{x}^{\frac{3}{4}}}-\dfrac{\class{steps-node}{\cssId{steps-node-13}{4}}\class{steps-node}{\cssId{steps-node-14}{{x}^{3}}}}{{x}^{8}}$

$=4{x}^{3}+\dfrac{1}{4{x}^{\frac{3}{4}}}-\dfrac{4}{{x}^{5}}$