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Pochodna funkcji cos(x/2)

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

$f\left(x\right) =$

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

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

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

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

$=-\class{steps-node}{\cssId{steps-node-4}{\dfrac{1}{2}}}{\cdot}\sin\left(\dfrac{x}{2}\right)$

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