gdzie jesteś: Start / Pochodne / Pochodne funkcji trygonometrycznych / Pochodna funkcji sin(x-y)

Pochodna funkcji sin(x-y)

$f\left(x, y\right) =$	$-\sin\left(y-x\right)$ Note: Your input has been rewritten/simplified.
$\dfrac{\mathrm{d}\left(f\left(x, y\right)\right)}{\mathrm{d}x} =$	$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(-\sin\left(y-x\right)\right)}}$ $=\class{steps-node}{\cssId{steps-node-2}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\sin\left(x-y\right)\right)}}$ $=\class{steps-node}{\cssId{steps-node-3}{\cos\left(x-y\right)}}{\cdot}\class{steps-node}{\cssId{steps-node-4}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(x-y\right)}}$ $=\class{steps-node}{\cssId{steps-node-5}{1}}{\cdot}\cos\left(x-y\right)$ $=\cos\left(x-y\right)$ Uproszczony wynik: $=\cos\left(y-x\right)$

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

$-\sin\left(y-x\right)$

Note: Your input has been rewritten/simplified.

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

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

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

$=\class{steps-node}{\cssId{steps-node-3}{\cos\left(x-y\right)}}{\cdot}\class{steps-node}{\cssId{steps-node-4}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(x-y\right)}}$

$=\class{steps-node}{\cssId{steps-node-5}{1}}{\cdot}\cos\left(x-y\right)$

$=\cos\left(x-y\right)$

Uproszczony wynik:

$=\cos\left(y-x\right)$