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Pochodna funkcji 1/2sin(2x)

$f\left(x\right) =$	$\dfrac{\sin\left(2x\right)}{2}$ Note: Your input has been rewritten/simplified.
$\dfrac{\mathrm{d}\left(f\left(x\right)\right)}{\mathrm{d}x} =$	$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\dfrac{\sin\left(2x\right)}{2}\right)}}$ $=\class{steps-node}{\cssId{steps-node-2}{\dfrac{\class{steps-node}{\cssId{steps-node-3}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\sin\left(2x\right)\right)}}}{2}}}$ $=\dfrac{\class{steps-node}{\cssId{steps-node-4}{\cos\left(2x\right)}}{\cdot}\class{steps-node}{\cssId{steps-node-5}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(2x\right)}}}{2}$ $=\dfrac{\class{steps-node}{\cssId{steps-node-6}{2}}{\cdot}\cos\left(2x\right)}{2}$ $=\cos\left(2x\right)$

$f\left(x\right) =$

$\dfrac{\sin\left(2x\right)}{2}$

Note: Your input has been rewritten/simplified.

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

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

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

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

$=\dfrac{\class{steps-node}{\cssId{steps-node-6}{2}}{\cdot}\cos\left(2x\right)}{2}$

$=\cos\left(2x\right)$