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Pochodna funkcji sqrt(3,x^2-1)-cos(7x^5+1/x)

$f\left(x\right) =$	${\left({x}^{2}-1\right)}^{\frac{1}{3}}-\cos\left(7{x}^{5}+\dfrac{1}{x}\right)$ Note: Your input has been rewritten/simplified.
$\dfrac{\mathrm{d}\left(f\left(x\right)\right)}{\mathrm{d}x} =$	$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({\left({x}^{2}-1\right)}^{\frac{1}{3}}-\cos\left(7{x}^{5}+\dfrac{1}{x}\right)\right)}}$ $=\class{steps-node}{\cssId{steps-node-2}{\class{steps-node}{\cssId{steps-node-3}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({\left({x}^{2}-1\right)}^{\frac{1}{3}}\right)}}-\class{steps-node}{\cssId{steps-node-4}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\cos\left(7{x}^{5}+\dfrac{1}{x}\right)\right)}}}}$ $=\class{steps-node}{\cssId{steps-node-5}{\dfrac{1}{3}}}{\cdot}\class{steps-node}{\cssId{steps-node-6}{{\left({x}^{2}-1\right)}^{\frac{1}{3}-1}}}{\cdot}\class{steps-node}{\cssId{steps-node-7}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({x}^{2}-1\right)}}-\class{steps-node}{\cssId{steps-node-8}{-\sin\left(7{x}^{5}+\dfrac{1}{x}\right)}}{\cdot}\class{steps-node}{\cssId{steps-node-9}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(7{x}^{5}+\dfrac{1}{x}\right)}}$ $=\class{steps-node}{\cssId{steps-node-11}{\left(7{\cdot}\class{steps-node}{\cssId{steps-node-12}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({x}^{5}\right)}}+\class{steps-node}{\cssId{steps-node-13}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\dfrac{1}{x}\right)}}\right)}}{\cdot}\sin\left(7{x}^{5}+\dfrac{1}{x}\right)+\dfrac{\class{steps-node}{\cssId{steps-node-10}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({x}^{2}\right)}}}{3{\cdot}{\left({x}^{2}-1\right)}^{\frac{2}{3}}}$ $=\left(\dfrac{\class{steps-node}{\cssId{steps-node-18}{-\class{steps-node}{\cssId{steps-node-17}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(x\right)}}}}}{\class{steps-node}{\cssId{steps-node-16}{{x}^{2}}}}+7{\cdot}\class{steps-node}{\cssId{steps-node-14}{5}}\class{steps-node}{\cssId{steps-node-15}{{x}^{4}}}\right){\cdot}\sin\left(7{x}^{5}+\dfrac{1}{x}\right)+\dfrac{\class{steps-node}{\cssId{steps-node-19}{2}}\class{steps-node}{\cssId{steps-node-20}{x}}}{3{\cdot}{\left({x}^{2}-1\right)}^{\frac{2}{3}}}$ $=\left(35{x}^{4}-\dfrac{\class{steps-node}{\cssId{steps-node-21}{1}}}{{x}^{2}}\right){\cdot}\sin\left(7{x}^{5}+\dfrac{1}{x}\right)+\dfrac{2x}{3{\cdot}{\left({x}^{2}-1\right)}^{\frac{2}{3}}}$

$f\left(x\right) =$

${\left({x}^{2}-1\right)}^{\frac{1}{3}}-\cos\left(7{x}^{5}+\dfrac{1}{x}\right)$

Note: Your input has been rewritten/simplified.

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

$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({\left({x}^{2}-1\right)}^{\frac{1}{3}}-\cos\left(7{x}^{5}+\dfrac{1}{x}\right)\right)}}$

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

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

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

$=\left(\dfrac{\class{steps-node}{\cssId{steps-node-18}{-\class{steps-node}{\cssId{steps-node-17}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(x\right)}}}}}{\class{steps-node}{\cssId{steps-node-16}{{x}^{2}}}}+7{\cdot}\class{steps-node}{\cssId{steps-node-14}{5}}\class{steps-node}{\cssId{steps-node-15}{{x}^{4}}}\right){\cdot}\sin\left(7{x}^{5}+\dfrac{1}{x}\right)+\dfrac{\class{steps-node}{\cssId{steps-node-19}{2}}\class{steps-node}{\cssId{steps-node-20}{x}}}{3{\cdot}{\left({x}^{2}-1\right)}^{\frac{2}{3}}}$

$=\left(35{x}^{4}-\dfrac{\class{steps-node}{\cssId{steps-node-21}{1}}}{{x}^{2}}\right){\cdot}\sin\left(7{x}^{5}+\dfrac{1}{x}\right)+\dfrac{2x}{3{\cdot}{\left({x}^{2}-1\right)}^{\frac{2}{3}}}$