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Pochodna funkcji 3*cos(x^2)

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

$f\left(x\right) =$

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

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

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

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

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

$=-3{\cdot}\class{steps-node}{\cssId{steps-node-6}{2}}\class{steps-node}{\cssId{steps-node-7}{x}}{\cdot}\sin\left({x}^{2}\right)$

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