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Pochodna funkcji sin(5x^5)

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

$f\left(x\right) =$

$\sin\left(5{x}^{5}\right)$

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

$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\sin\left(5{x}^{5}\right)\right)}}$

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

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

$=5{\cdot}\class{steps-node}{\cssId{steps-node-6}{5}}\class{steps-node}{\cssId{steps-node-7}{{x}^{4}}}{\cdot}\cos\left(5{x}^{5}\right)$

$=25{x}^{4}{\cdot}\cos\left(5{x}^{5}\right)$