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Pochodna funkcji (a)sin(a/x)

$f\left(a, x\right) =$	$a{\cdot}\sin\left(\dfrac{a}{x}\right)$
$\dfrac{\mathrm{d}\left(f\left(a, x\right)\right)}{\mathrm{d}x} =$	$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(a{\cdot}\sin\left(\dfrac{a}{x}\right)\right)}}$ $=\class{steps-node}{\cssId{steps-node-2}{a{\cdot}\class{steps-node}{\cssId{steps-node-3}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\sin\left(\dfrac{a}{x}\right)\right)}}}}$ $=a{\cdot}\class{steps-node}{\cssId{steps-node-4}{\cos\left(\dfrac{a}{x}\right)}}{\cdot}\class{steps-node}{\cssId{steps-node-5}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\dfrac{a}{x}\right)}}$ $=a{\cdot}\class{steps-node}{\cssId{steps-node-6}{a{\cdot}\class{steps-node}{\cssId{steps-node-7}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\dfrac{1}{x}\right)}}}}{\cdot}\cos\left(\dfrac{a}{x}\right)$ $={a}^{2}{\cdot}\dfrac{\class{steps-node}{\cssId{steps-node-10}{-\class{steps-node}{\cssId{steps-node-9}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(x\right)}}}}}{\class{steps-node}{\cssId{steps-node-8}{{x}^{2}}}}{\cdot}\cos\left(\dfrac{a}{x}\right)$ $=\dfrac{-{a}^{2}{\cdot}\class{steps-node}{\cssId{steps-node-11}{1}}{\cdot}\cos\left(\dfrac{a}{x}\right)}{{x}^{2}}$ $=\dfrac{-{a}^{2}{\cdot}\cos\left(\dfrac{a}{x}\right)}{{x}^{2}}$

$f\left(a, x\right) =$

$a{\cdot}\sin\left(\dfrac{a}{x}\right)$

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

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

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

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

$=a{\cdot}\class{steps-node}{\cssId{steps-node-6}{a{\cdot}\class{steps-node}{\cssId{steps-node-7}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\dfrac{1}{x}\right)}}}}{\cdot}\cos\left(\dfrac{a}{x}\right)$

$={a}^{2}{\cdot}\dfrac{\class{steps-node}{\cssId{steps-node-10}{-\class{steps-node}{\cssId{steps-node-9}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(x\right)}}}}}{\class{steps-node}{\cssId{steps-node-8}{{x}^{2}}}}{\cdot}\cos\left(\dfrac{a}{x}\right)$

$=\dfrac{-{a}^{2}{\cdot}\class{steps-node}{\cssId{steps-node-11}{1}}{\cdot}\cos\left(\dfrac{a}{x}\right)}{{x}^{2}}$

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