gdzie jesteś: Start / Pochodne / Pochodne funkcji trygonometrycznych / Pochodna funkcji 3cos(4x)

Pochodna funkcji 3cos(4x)

$f\left(x\right) =$	$3{\cdot}\cos\left(4x\right)$
$\dfrac{\mathrm{d}\left(f\left(x\right)\right)}{\mathrm{d}x} =$	$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(3{\cdot}\cos\left(4x\right)\right)}}$ $=\class{steps-node}{\cssId{steps-node-2}{3{\cdot}\class{steps-node}{\cssId{steps-node-3}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\cos\left(4x\right)\right)}}}}$ $=3{\cdot}\class{steps-node}{\cssId{steps-node-4}{-\sin\left(4x\right)}}{\cdot}\class{steps-node}{\cssId{steps-node-5}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(4x\right)}}$ $=-3{\cdot}\class{steps-node}{\cssId{steps-node-6}{4}}{\cdot}\sin\left(4x\right)$ $=-12{\cdot}\sin\left(4x\right)$

$f\left(x\right) =$

$3{\cdot}\cos\left(4x\right)$

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

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

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

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

$=-3{\cdot}\class{steps-node}{\cssId{steps-node-6}{4}}{\cdot}\sin\left(4x\right)$

$=-12{\cdot}\sin\left(4x\right)$