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Pochodna funkcji sin(12/x+5)

$f\left(x\right) =$	$\sin\left(\dfrac{12}{x}+5\right)$
$\dfrac{\mathrm{d}}{\mathrm{d}x}f\left(x\right) =$	$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\sin\left(\dfrac{12}{x}+5\right)\right)}}$ $=\class{steps-node}{\cssId{steps-node-2}{\cos\left(\dfrac{12}{x}+5\right)}}{\cdot}\class{steps-node}{\cssId{steps-node-3}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\dfrac{12}{x}+5\right)}}$ $=\class{steps-node}{\cssId{steps-node-4}{12{\cdot}\class{steps-node}{\cssId{steps-node-5}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\dfrac{1}{x}\right)}}}}{\cdot}\cos\left(\dfrac{12}{x}+5\right)$ $=12{\cdot}\dfrac{\class{steps-node}{\cssId{steps-node-8}{-\class{steps-node}{\cssId{steps-node-7}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(x\right)}}}}}{\class{steps-node}{\cssId{steps-node-6}{{x}^{2}}}}{\cdot}\cos\left(\dfrac{12}{x}+5\right)$ $=\dfrac{-12{\cdot}\class{steps-node}{\cssId{steps-node-9}{1}}{\cdot}\cos\left(\dfrac{12}{x}+5\right)}{{x}^{2}}$ $=\dfrac{-12{\cdot}\cos\left(\dfrac{12}{x}+5\right)}{{x}^{2}}$

$f\left(x\right) =$

$\sin\left(\dfrac{12}{x}+5\right)$

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

$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\sin\left(\dfrac{12}{x}+5\right)\right)}}$

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

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

$=12{\cdot}\dfrac{\class{steps-node}{\cssId{steps-node-8}{-\class{steps-node}{\cssId{steps-node-7}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(x\right)}}}}}{\class{steps-node}{\cssId{steps-node-6}{{x}^{2}}}}{\cdot}\cos\left(\dfrac{12}{x}+5\right)$

$=\dfrac{-12{\cdot}\class{steps-node}{\cssId{steps-node-9}{1}}{\cdot}\cos\left(\dfrac{12}{x}+5\right)}{{x}^{2}}$

$=\dfrac{-12{\cdot}\cos\left(\dfrac{12}{x}+5\right)}{{x}^{2}}$