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Pochodna funkcji -cosx^2/y^2

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

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

$\dfrac{-{\left(\cos\left(x\right)\right)}^{2}}{{y}^{2}}$

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

$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\dfrac{-{\left(\cos\left(x\right)\right)}^{2}}{{y}^{2}}\right)}}$

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

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

$=\dfrac{-2{\cdot}\class{steps-node}{\cssId{steps-node-7}{\left(-\sin\left(x\right)\right)}}{\cdot}\cos\left(x\right)}{{y}^{2}}$

$=\dfrac{2{\cdot}\cos\left(x\right){\cdot}\sin\left(x\right)}{{y}^{2}}$