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Pochodna funkcji sin(x-1)

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

$f\left(x\right) =$

$\sin\left(x-1\right)$

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

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

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

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

$=\cos\left(x-1\right)$