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Pochodna funkcji [sin(2x)]^6

$f\left(x\right) =$	${\left(\sin\left(2x\right)\right)}^{6}$
$\dfrac{\mathrm{d}\left(f\left(x\right)\right)}{\mathrm{d}x} =$	$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({\left(\sin\left(2x\right)\right)}^{6}\right)}}$ $=\class{steps-node}{\cssId{steps-node-2}{6}}{\cdot}\class{steps-node}{\cssId{steps-node-3}{{\left(\sin\left(2x\right)\right)}^{5}}}{\cdot}\class{steps-node}{\cssId{steps-node-4}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\sin\left(2x\right)\right)}}$ $=6{\cdot}\class{steps-node}{\cssId{steps-node-5}{\cos\left(2x\right)}}{\cdot}\class{steps-node}{\cssId{steps-node-6}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(2x\right)}}{\cdot}{\left(\sin\left(2x\right)\right)}^{5}$ $=6{\cdot}\class{steps-node}{\cssId{steps-node-7}{2}}{\cdot}\cos\left(2x\right){\cdot}{\left(\sin\left(2x\right)\right)}^{5}$ $=12{\cdot}\cos\left(2x\right){\cdot}{\left(\sin\left(2x\right)\right)}^{5}$

$f\left(x\right) =$

${\left(\sin\left(2x\right)\right)}^{6}$

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

$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({\left(\sin\left(2x\right)\right)}^{6}\right)}}$

$=\class{steps-node}{\cssId{steps-node-2}{6}}{\cdot}\class{steps-node}{\cssId{steps-node-3}{{\left(\sin\left(2x\right)\right)}^{5}}}{\cdot}\class{steps-node}{\cssId{steps-node-4}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\sin\left(2x\right)\right)}}$

$=6{\cdot}\class{steps-node}{\cssId{steps-node-5}{\cos\left(2x\right)}}{\cdot}\class{steps-node}{\cssId{steps-node-6}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(2x\right)}}{\cdot}{\left(\sin\left(2x\right)\right)}^{5}$

$=6{\cdot}\class{steps-node}{\cssId{steps-node-7}{2}}{\cdot}\cos\left(2x\right){\cdot}{\left(\sin\left(2x\right)\right)}^{5}$

$=12{\cdot}\cos\left(2x\right){\cdot}{\left(\sin\left(2x\right)\right)}^{5}$