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Pochodna funkcji e^x*cosy

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

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

${\mathrm{e}}^{x}{\cdot}\cos\left(y\right)$

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

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

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

$=\class{steps-node}{\cssId{steps-node-4}{{\mathrm{e}}^{x}}}{\cdot}\cos\left(y\right)$

$=\cos\left(y\right){\cdot}{\mathrm{e}}^{x}$

Uproszczony wynik:

$={\mathrm{e}}^{x}{\cdot}\cos\left(y\right)$