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Pochodna funkcji (cos(x)^2)((2x)+6)

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

$f\left(x\right) =$

$\left(2x+6\right){\cdot}{\left(\cos\left(x\right)\right)}^{2}$

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

$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\left(2x+6\right){\cdot}{\left(\cos\left(x\right)\right)}^{2}\right)}}$

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

$=\class{steps-node}{\cssId{steps-node-6}{2}}{\cdot}{\left(\cos\left(x\right)\right)}^{2}+\class{steps-node}{\cssId{steps-node-7}{2}}{\cdot}\class{steps-node}{\cssId{steps-node-8}{\cos\left(x\right)}}{\cdot}\class{steps-node}{\cssId{steps-node-9}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\cos\left(x\right)\right)}}{\cdot}\left(2x+6\right)$

$=2{\cdot}{\left(\cos\left(x\right)\right)}^{2}+2{\cdot}\class{steps-node}{\cssId{steps-node-10}{\left(-\sin\left(x\right)\right)}}{\cdot}\left(2x+6\right){\cdot}\cos\left(x\right)$

$=2{\cdot}{\left(\cos\left(x\right)\right)}^{2}-2{\cdot}\left(2x+6\right){\cdot}\cos\left(x\right){\cdot}\sin\left(x\right)$