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Pochodna funkcji sqrt(x)*cos(x)

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

$f\left(x\right) =$

$\sqrt{x}{\cdot}\cos\left(x\right)$

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

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

$=\class{steps-node}{\cssId{steps-node-3}{\class{steps-node}{\cssId{steps-node-2}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\sqrt{x}\right)}}{\cdot}\cos\left(x\right)}}+\class{steps-node}{\cssId{steps-node-5}{\sqrt{x}{\cdot}\class{steps-node}{\cssId{steps-node-4}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\cos\left(x\right)\right)}}}}$

$=\class{steps-node}{\cssId{steps-node-6}{\dfrac{1}{2{\cdot}\sqrt{x}}}}{\cdot}\cos\left(x\right)+\class{steps-node}{\cssId{steps-node-7}{-\sin\left(x\right)}}{\cdot}\sqrt{x}$

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