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Pochodna funkcji 3cos(x)cos(x)+1

$f\left(x\right) =$	$3{\cdot}{\left(\cos\left(x\right)\right)}^{2}+1$
	Note: Your input has been rewritten/simplified.
$\dfrac{\mathrm{d}\left(f\left(x\right)\right)}{\mathrm{d}x} =$	$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathbf{d}}{\mathbf{d}\boldsymbol{x}}\kern-.25em\left(3{\cdot}{\left(\cos\left(x\right)\right)}^{2}+1\right)}}$ $=\class{steps-node}{\cssId{steps-node-2}{3{\cdot}\class{steps-node}{\cssId{steps-node-3}{\tfrac{\mathbf{d}}{\mathbf{d}\boldsymbol{x}}\kern-.25em\left({\left(\cos\left(x\right)\right)}^{2}\right)}}}}$ $=3{\cdot}\class{steps-node}{\cssId{steps-node-4}{2}}{\cdot}\class{steps-node}{\cssId{steps-node-5}{\cos\left(x\right)}}{\cdot}\class{steps-node}{\cssId{steps-node-6}{\tfrac{\mathbf{d}}{\mathbf{d}\boldsymbol{x}}\kern-.25em\left(\cos\left(x\right)\right)}}$ $=6{\cdot}\class{steps-node}{\cssId{steps-node-7}{\left(-\sin\left(x\right)\right)}}{\cdot}\cos\left(x\right)$ $=-6{\cdot}\cos\left(x\right){\cdot}\sin\left(x\right)$

$f\left(x\right) =$

$3{\cdot}{\left(\cos\left(x\right)\right)}^{2}+1$

Note: Your input has been rewritten/simplified.

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

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

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

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

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

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