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Pochodna funkcji x^1/3*cos(3x+1)

$f\left(x\right) =$	$\dfrac{x{\cdot}\cos\left(3x+1\right)}{3}$
$\dfrac{\mathrm{d}\left(f\left(x\right)\right)}{\mathrm{d}x} =$	$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\dfrac{x{\cdot}\cos\left(3x+1\right)}{3}\right)}}$ $=\class{steps-node}{\cssId{steps-node-2}{\dfrac{\class{steps-node}{\cssId{steps-node-3}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(x{\cdot}\cos\left(3x+1\right)\right)}}}{3}}}$ $=\dfrac{\class{steps-node}{\cssId{steps-node-5}{\class{steps-node}{\cssId{steps-node-4}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(x\right)}}{\cdot}\cos\left(3x+1\right)}}+\class{steps-node}{\cssId{steps-node-7}{x{\cdot}\class{steps-node}{\cssId{steps-node-6}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\cos\left(3x+1\right)\right)}}}}}{3}$ $=\dfrac{\class{steps-node}{\cssId{steps-node-8}{1}}{\cdot}\cos\left(3x+1\right)+\class{steps-node}{\cssId{steps-node-9}{-\sin\left(3x+1\right)}}{\cdot}\class{steps-node}{\cssId{steps-node-10}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(3x+1\right)}}{\cdot}x}{3}$ $=\dfrac{\cos\left(3x+1\right)-\class{steps-node}{\cssId{steps-node-11}{3}}x{\cdot}\sin\left(3x+1\right)}{3}$ Uproszczony wynik: $=\dfrac{\cos\left(3x+1\right)}{3}-x{\cdot}\sin\left(3x+1\right)$

$f\left(x\right) =$

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

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

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

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

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

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

$=\dfrac{\cos\left(3x+1\right)-\class{steps-node}{\cssId{steps-node-11}{3}}x{\cdot}\sin\left(3x+1\right)}{3}$

Uproszczony wynik:

$=\dfrac{\cos\left(3x+1\right)}{3}-x{\cdot}\sin\left(3x+1\right)$