gdzie jesteś: Start / Pochodne / Pochodne funkcji trygonometrycznych / Pochodna funkcji sinxcosx

Pochodna funkcji sinxcosx

$f\left(x\right) =$	$\cos\left(x\right){\cdot}\sin\left(x\right)$
	Note: Your input has been rewritten/simplified.
$\dfrac{\mathrm{d}\left(f\left(x\right)\right)}{\mathrm{d}x} =$	$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathbf{d}}{\mathbf{d}\boldsymbol{x}}\kern-.25em\left(\cos\left(x\right){\cdot}\sin\left(x\right)\right)}}$ $=\class{steps-node}{\cssId{steps-node-3}{\class{steps-node}{\cssId{steps-node-2}{\tfrac{\mathbf{d}}{\mathbf{d}\boldsymbol{x}}\kern-.25em\left(\cos\left(x\right)\right)}}{\cdot}\sin\left(x\right)}}+\class{steps-node}{\cssId{steps-node-5}{\cos\left(x\right){\cdot}\class{steps-node}{\cssId{steps-node-4}{\tfrac{\mathbf{d}}{\mathbf{d}\boldsymbol{x}}\kern-.25em\left(\sin\left(x\right)\right)}}}}$ $=\class{steps-node}{\cssId{steps-node-6}{-\sin\left(x\right)}}{\cdot}\sin\left(x\right)+\class{steps-node}{\cssId{steps-node-7}{\cos\left(x\right)}}{\cdot}\cos\left(x\right)$ $={\left(\cos\left(x\right)\right)}^{2}-{\left(\sin\left(x\right)\right)}^{2}$

$f\left(x\right) =$

$\cos\left(x\right){\cdot}\sin\left(x\right)$

Note: Your input has been rewritten/simplified.

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

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

$=\class{steps-node}{\cssId{steps-node-3}{\class{steps-node}{\cssId{steps-node-2}{\tfrac{\mathbf{d}}{\mathbf{d}\boldsymbol{x}}\kern-.25em\left(\cos\left(x\right)\right)}}{\cdot}\sin\left(x\right)}}+\class{steps-node}{\cssId{steps-node-5}{\cos\left(x\right){\cdot}\class{steps-node}{\cssId{steps-node-4}{\tfrac{\mathbf{d}}{\mathbf{d}\boldsymbol{x}}\kern-.25em\left(\sin\left(x\right)\right)}}}}$

$=\class{steps-node}{\cssId{steps-node-6}{-\sin\left(x\right)}}{\cdot}\sin\left(x\right)+\class{steps-node}{\cssId{steps-node-7}{\cos\left(x\right)}}{\cdot}\cos\left(x\right)$

$={\left(\cos\left(x\right)\right)}^{2}-{\left(\sin\left(x\right)\right)}^{2}$