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Pochodna funkcji Sin(x+1)+cos(x+1)

$f\left(x\right) =$	$\sin\left(x+1\right)+\cos\left(x+1\right)$
$\dfrac{\mathrm{d}\left(f\left(x\right)\right)}{\mathrm{d}x} =$	$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathbf{d}}{\mathbf{d}\boldsymbol{x}}\kern-.25em\left(\sin\left(x+1\right)+\cos\left(x+1\right)\right)}}$ $=\class{steps-node}{\cssId{steps-node-2}{\class{steps-node}{\cssId{steps-node-3}{\tfrac{\mathbf{d}}{\mathbf{d}\boldsymbol{x}}\kern-.25em\left(\sin\left(x+1\right)\right)}}+\class{steps-node}{\cssId{steps-node-4}{\tfrac{\mathbf{d}}{\mathbf{d}\boldsymbol{x}}\kern-.25em\left(\cos\left(x+1\right)\right)}}}}$ $=\class{steps-node}{\cssId{steps-node-7}{-\sin\left(x+1\right)}}{\cdot}\class{steps-node}{\cssId{steps-node-8}{\tfrac{\mathbf{d}}{\mathbf{d}\boldsymbol{x}}\kern-.25em\left(x+1\right)}}+\class{steps-node}{\cssId{steps-node-5}{\cos\left(x+1\right)}}{\cdot}\class{steps-node}{\cssId{steps-node-6}{\tfrac{\mathbf{d}}{\mathbf{d}\boldsymbol{x}}\kern-.25em\left(x+1\right)}}$ $=\class{steps-node}{\cssId{steps-node-10}{1}}{\cdot}\cos\left(x+1\right)-\class{steps-node}{\cssId{steps-node-9}{1}}{\cdot}\sin\left(x+1\right)$ $=\cos\left(x+1\right)-\sin\left(x+1\right)$

$f\left(x\right) =$

$\sin\left(x+1\right)+\cos\left(x+1\right)$

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

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

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

$=\class{steps-node}{\cssId{steps-node-7}{-\sin\left(x+1\right)}}{\cdot}\class{steps-node}{\cssId{steps-node-8}{\tfrac{\mathbf{d}}{\mathbf{d}\boldsymbol{x}}\kern-.25em\left(x+1\right)}}+\class{steps-node}{\cssId{steps-node-5}{\cos\left(x+1\right)}}{\cdot}\class{steps-node}{\cssId{steps-node-6}{\tfrac{\mathbf{d}}{\mathbf{d}\boldsymbol{x}}\kern-.25em\left(x+1\right)}}$

$=\class{steps-node}{\cssId{steps-node-10}{1}}{\cdot}\cos\left(x+1\right)-\class{steps-node}{\cssId{steps-node-9}{1}}{\cdot}\sin\left(x+1\right)$

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