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Pochodna funkcji 72tan(x)-72tan(x)cos(4x)

$f\left(x\right) =$	$72{\cdot}\tan\left(x\right)-72{\cdot}\tan\left(x\right){\cdot}\cos\left(4x\right)$
$\dfrac{\mathrm{d}\left(f\left(x\right)\right)}{\mathrm{d}x} =$	$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(72{\cdot}\tan\left(x\right)-72{\cdot}\tan\left(x\right){\cdot}\cos\left(4x\right)\right)}}$ $=\class{steps-node}{\cssId{steps-node-2}{72{\cdot}\class{steps-node}{\cssId{steps-node-3}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\tan\left(x\right)\right)}}-72{\cdot}\class{steps-node}{\cssId{steps-node-4}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\tan\left(x\right){\cdot}\cos\left(4x\right)\right)}}}}$ $=72{\cdot}\class{steps-node}{\cssId{steps-node-5}{{\left(\sec\left(x\right)\right)}^{2}}}-72{\cdot}\left(\class{steps-node}{\cssId{steps-node-7}{\class{steps-node}{\cssId{steps-node-6}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\tan\left(x\right)\right)}}{\cdot}\cos\left(4x\right)}}+\class{steps-node}{\cssId{steps-node-9}{\tan\left(x\right){\cdot}\class{steps-node}{\cssId{steps-node-8}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\cos\left(4x\right)\right)}}}}\right)$ $=72{\cdot}{\left(\sec\left(x\right)\right)}^{2}-72{\cdot}\left(\class{steps-node}{\cssId{steps-node-10}{{\left(\sec\left(x\right)\right)}^{2}}}{\cdot}\cos\left(4x\right)+\class{steps-node}{\cssId{steps-node-11}{-\sin\left(4x\right)}}{\cdot}\class{steps-node}{\cssId{steps-node-12}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(4x\right)}}{\cdot}\tan\left(x\right)\right)$ $=72{\cdot}{\left(\sec\left(x\right)\right)}^{2}-72{\cdot}\left({\left(\sec\left(x\right)\right)}^{2}{\cdot}\cos\left(4x\right)-\class{steps-node}{\cssId{steps-node-13}{4}}{\cdot}\tan\left(x\right){\cdot}\sin\left(4x\right)\right)$ Wynik alternatywny: $=288{\cdot}\tan\left(x\right){\cdot}\sin\left(4x\right)-72{\cdot}{\left(\sec\left(x\right)\right)}^{2}{\cdot}\cos\left(4x\right)+72{\cdot}{\left(\sec\left(x\right)\right)}^{2}$

$f\left(x\right) =$

$72{\cdot}\tan\left(x\right)-72{\cdot}\tan\left(x\right){\cdot}\cos\left(4x\right)$

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

$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(72{\cdot}\tan\left(x\right)-72{\cdot}\tan\left(x\right){\cdot}\cos\left(4x\right)\right)}}$

$=\class{steps-node}{\cssId{steps-node-2}{72{\cdot}\class{steps-node}{\cssId{steps-node-3}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\tan\left(x\right)\right)}}-72{\cdot}\class{steps-node}{\cssId{steps-node-4}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\tan\left(x\right){\cdot}\cos\left(4x\right)\right)}}}}$

$=72{\cdot}\class{steps-node}{\cssId{steps-node-5}{{\left(\sec\left(x\right)\right)}^{2}}}-72{\cdot}\left(\class{steps-node}{\cssId{steps-node-7}{\class{steps-node}{\cssId{steps-node-6}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\tan\left(x\right)\right)}}{\cdot}\cos\left(4x\right)}}+\class{steps-node}{\cssId{steps-node-9}{\tan\left(x\right){\cdot}\class{steps-node}{\cssId{steps-node-8}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\cos\left(4x\right)\right)}}}}\right)$

$=72{\cdot}{\left(\sec\left(x\right)\right)}^{2}-72{\cdot}\left(\class{steps-node}{\cssId{steps-node-10}{{\left(\sec\left(x\right)\right)}^{2}}}{\cdot}\cos\left(4x\right)+\class{steps-node}{\cssId{steps-node-11}{-\sin\left(4x\right)}}{\cdot}\class{steps-node}{\cssId{steps-node-12}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(4x\right)}}{\cdot}\tan\left(x\right)\right)$

$=72{\cdot}{\left(\sec\left(x\right)\right)}^{2}-72{\cdot}\left({\left(\sec\left(x\right)\right)}^{2}{\cdot}\cos\left(4x\right)-\class{steps-node}{\cssId{steps-node-13}{4}}{\cdot}\tan\left(x\right){\cdot}\sin\left(4x\right)\right)$

Wynik alternatywny:

$=288{\cdot}\tan\left(x\right){\cdot}\sin\left(4x\right)-72{\cdot}{\left(\sec\left(x\right)\right)}^{2}{\cdot}\cos\left(4x\right)+72{\cdot}{\left(\sec\left(x\right)\right)}^{2}$