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Pochodna funkcji 64(sinx*cosx)^6

$f\left(x\right) =$	$64{\cdot}{\left(\cos\left(x\right)\right)}^{6}{\cdot}{\left(\sin\left(x\right)\right)}^{6}$ Note: Your input has been rewritten/simplified.
$\dfrac{\mathrm{d}\left(f\left(x\right)\right)}{\mathrm{d}x} =$	$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(64{\cdot}{\left(\cos\left(x\right)\right)}^{6}{\cdot}{\left(\sin\left(x\right)\right)}^{6}\right)}}$ $=\class{steps-node}{\cssId{steps-node-2}{64{\cdot}\class{steps-node}{\cssId{steps-node-3}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({\left(\cos\left(x\right)\right)}^{6}{\cdot}{\left(\sin\left(x\right)\right)}^{6}\right)}}}}$ $=64{\cdot}\left(\class{steps-node}{\cssId{steps-node-5}{\class{steps-node}{\cssId{steps-node-4}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({\left(\cos\left(x\right)\right)}^{6}\right)}}{\cdot}{\left(\sin\left(x\right)\right)}^{6}}}+\class{steps-node}{\cssId{steps-node-7}{{\left(\cos\left(x\right)\right)}^{6}{\cdot}\class{steps-node}{\cssId{steps-node-6}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({\left(\sin\left(x\right)\right)}^{6}\right)}}}}\right)$ $=64{\cdot}\left(\class{steps-node}{\cssId{steps-node-8}{6}}{\cdot}\class{steps-node}{\cssId{steps-node-9}{{\left(\cos\left(x\right)\right)}^{5}}}{\cdot}\class{steps-node}{\cssId{steps-node-10}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\cos\left(x\right)\right)}}{\cdot}{\left(\sin\left(x\right)\right)}^{6}+\class{steps-node}{\cssId{steps-node-11}{6}}{\cdot}\class{steps-node}{\cssId{steps-node-12}{{\left(\sin\left(x\right)\right)}^{5}}}{\cdot}\class{steps-node}{\cssId{steps-node-13}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\sin\left(x\right)\right)}}{\cdot}{\left(\cos\left(x\right)\right)}^{6}\right)$ $=64{\cdot}\left(6{\cdot}\class{steps-node}{\cssId{steps-node-14}{\left(-\sin\left(x\right)\right)}}{\cdot}{\left(\cos\left(x\right)\right)}^{5}{\cdot}{\left(\sin\left(x\right)\right)}^{6}+6{\cdot}\class{steps-node}{\cssId{steps-node-15}{\cos\left(x\right)}}{\cdot}{\left(\cos\left(x\right)\right)}^{6}{\cdot}{\left(\sin\left(x\right)\right)}^{5}\right)$ $=64{\cdot}\left(6{\cdot}{\left(\cos\left(x\right)\right)}^{7}{\cdot}{\left(\sin\left(x\right)\right)}^{5}-6{\cdot}{\left(\cos\left(x\right)\right)}^{5}{\cdot}{\left(\sin\left(x\right)\right)}^{7}\right)$ Wynik alternatywny: $=384{\cdot}{\left(\cos\left(x\right)\right)}^{7}{\cdot}{\left(\sin\left(x\right)\right)}^{5}-384{\cdot}{\left(\cos\left(x\right)\right)}^{5}{\cdot}{\left(\sin\left(x\right)\right)}^{7}$

$f\left(x\right) =$

$64{\cdot}{\left(\cos\left(x\right)\right)}^{6}{\cdot}{\left(\sin\left(x\right)\right)}^{6}$

Note: Your input has been rewritten/simplified.

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

$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(64{\cdot}{\left(\cos\left(x\right)\right)}^{6}{\cdot}{\left(\sin\left(x\right)\right)}^{6}\right)}}$

$=\class{steps-node}{\cssId{steps-node-2}{64{\cdot}\class{steps-node}{\cssId{steps-node-3}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({\left(\cos\left(x\right)\right)}^{6}{\cdot}{\left(\sin\left(x\right)\right)}^{6}\right)}}}}$

$=64{\cdot}\left(\class{steps-node}{\cssId{steps-node-5}{\class{steps-node}{\cssId{steps-node-4}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({\left(\cos\left(x\right)\right)}^{6}\right)}}{\cdot}{\left(\sin\left(x\right)\right)}^{6}}}+\class{steps-node}{\cssId{steps-node-7}{{\left(\cos\left(x\right)\right)}^{6}{\cdot}\class{steps-node}{\cssId{steps-node-6}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({\left(\sin\left(x\right)\right)}^{6}\right)}}}}\right)$

$=64{\cdot}\left(\class{steps-node}{\cssId{steps-node-8}{6}}{\cdot}\class{steps-node}{\cssId{steps-node-9}{{\left(\cos\left(x\right)\right)}^{5}}}{\cdot}\class{steps-node}{\cssId{steps-node-10}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\cos\left(x\right)\right)}}{\cdot}{\left(\sin\left(x\right)\right)}^{6}+\class{steps-node}{\cssId{steps-node-11}{6}}{\cdot}\class{steps-node}{\cssId{steps-node-12}{{\left(\sin\left(x\right)\right)}^{5}}}{\cdot}\class{steps-node}{\cssId{steps-node-13}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\sin\left(x\right)\right)}}{\cdot}{\left(\cos\left(x\right)\right)}^{6}\right)$

$=64{\cdot}\left(6{\cdot}\class{steps-node}{\cssId{steps-node-14}{\left(-\sin\left(x\right)\right)}}{\cdot}{\left(\cos\left(x\right)\right)}^{5}{\cdot}{\left(\sin\left(x\right)\right)}^{6}+6{\cdot}\class{steps-node}{\cssId{steps-node-15}{\cos\left(x\right)}}{\cdot}{\left(\cos\left(x\right)\right)}^{6}{\cdot}{\left(\sin\left(x\right)\right)}^{5}\right)$

$=64{\cdot}\left(6{\cdot}{\left(\cos\left(x\right)\right)}^{7}{\cdot}{\left(\sin\left(x\right)\right)}^{5}-6{\cdot}{\left(\cos\left(x\right)\right)}^{5}{\cdot}{\left(\sin\left(x\right)\right)}^{7}\right)$

Wynik alternatywny:

$=384{\cdot}{\left(\cos\left(x\right)\right)}^{7}{\cdot}{\left(\sin\left(x\right)\right)}^{5}-384{\cdot}{\left(\cos\left(x\right)\right)}^{5}{\cdot}{\left(\sin\left(x\right)\right)}^{7}$