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Pochodna funkcji (cosx)^3

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

$f\left(x\right) =$

${\left(\cos\left(x\right)\right)}^{3}$

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

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

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

$=3{\cdot}\class{steps-node}{\cssId{steps-node-5}{\left(-\sin\left(x\right)\right)}}{\cdot}{\left(\cos\left(x\right)\right)}^{2}$

$=-3{\cdot}{\left(\cos\left(x\right)\right)}^{2}{\cdot}\sin\left(x\right)$