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Pochodna funkcji 8sin(x)+8cos(x)

$f\left(x\right) =$	$8{\cdot}\sin\left(x\right)+8{\cdot}\cos\left(x\right)$
$\dfrac{\mathrm{d}\left(f\left(x\right)\right)}{\mathrm{d}x} =$	$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathbf{d}}{\mathbf{d}\boldsymbol{x}}\kern-.25em\left(8{\cdot}\sin\left(x\right)+8{\cdot}\cos\left(x\right)\right)}}$ $=\class{steps-node}{\cssId{steps-node-2}{8{\cdot}\class{steps-node}{\cssId{steps-node-3}{\tfrac{\mathbf{d}}{\mathbf{d}\boldsymbol{x}}\kern-.25em\left(\sin\left(x\right)\right)}}+8{\cdot}\class{steps-node}{\cssId{steps-node-4}{\tfrac{\mathbf{d}}{\mathbf{d}\boldsymbol{x}}\kern-.25em\left(\cos\left(x\right)\right)}}}}$ $=8{\cdot}\class{steps-node}{\cssId{steps-node-6}{\left(-\sin\left(x\right)\right)}}+8{\cdot}\class{steps-node}{\cssId{steps-node-5}{\cos\left(x\right)}}$ $=8{\cdot}\cos\left(x\right)-8{\cdot}\sin\left(x\right)$

$f\left(x\right) =$

$8{\cdot}\sin\left(x\right)+8{\cdot}\cos\left(x\right)$

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

$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathbf{d}}{\mathbf{d}\boldsymbol{x}}\kern-.25em\left(8{\cdot}\sin\left(x\right)+8{\cdot}\cos\left(x\right)\right)}}$

$=\class{steps-node}{\cssId{steps-node-2}{8{\cdot}\class{steps-node}{\cssId{steps-node-3}{\tfrac{\mathbf{d}}{\mathbf{d}\boldsymbol{x}}\kern-.25em\left(\sin\left(x\right)\right)}}+8{\cdot}\class{steps-node}{\cssId{steps-node-4}{\tfrac{\mathbf{d}}{\mathbf{d}\boldsymbol{x}}\kern-.25em\left(\cos\left(x\right)\right)}}}}$

$=8{\cdot}\class{steps-node}{\cssId{steps-node-6}{\left(-\sin\left(x\right)\right)}}+8{\cdot}\class{steps-node}{\cssId{steps-node-5}{\cos\left(x\right)}}$

$=8{\cdot}\cos\left(x\right)-8{\cdot}\sin\left(x\right)$