gdzie jesteś: Start / Pochodne / Pochodne funkcji trygonometrycznych / Pochodna funkcji sin(5-x)

Pochodna funkcji sin(5-x)

$f\left(x\right) =$	$-\sin\left(x-5\right)$
	Note: Your input has been rewritten/simplified.
$\dfrac{\mathrm{d}\left(f\left(x\right)\right)}{\mathrm{d}x} =$	$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathbf{d}}{\mathbf{d}\boldsymbol{x}}\kern-.25em\left(-\sin\left(x-5\right)\right)}}$ $=\class{steps-node}{\cssId{steps-node-2}{-\class{steps-node}{\cssId{steps-node-3}{\tfrac{\mathbf{d}}{\mathbf{d}\boldsymbol{x}}\kern-.25em\left(\sin\left(x-5\right)\right)}}}}$ $=-\left(\class{steps-node}{\cssId{steps-node-4}{\cos\left(x-5\right)}}{\cdot}\class{steps-node}{\cssId{steps-node-5}{\tfrac{\mathbf{d}}{\mathbf{d}\boldsymbol{x}}\kern-.25em\left(x-5\right)}}\right)$ $=-\class{steps-node}{\cssId{steps-node-6}{1}}{\cdot}\cos\left(x-5\right)$ $=-\cos\left(x-5\right)$

$f\left(x\right) =$

$-\sin\left(x-5\right)$

Note: Your input has been rewritten/simplified.

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

$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathbf{d}}{\mathbf{d}\boldsymbol{x}}\kern-.25em\left(-\sin\left(x-5\right)\right)}}$

$=\class{steps-node}{\cssId{steps-node-2}{-\class{steps-node}{\cssId{steps-node-3}{\tfrac{\mathbf{d}}{\mathbf{d}\boldsymbol{x}}\kern-.25em\left(\sin\left(x-5\right)\right)}}}}$

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

$=-\class{steps-node}{\cssId{steps-node-6}{1}}{\cdot}\cos\left(x-5\right)$

$=-\cos\left(x-5\right)$