Matematyka
Pochodna funkcji 1-sinx*cosx
| $f\left(x\right) =$ |
$1-\cos\left(x\right){\cdot}\sin\left(x\right)$
Note: Your input has been rewritten/simplified. |
|---|---|
| $\dfrac{\mathrm{d}\left(f\left(x\right)\right)}{\mathrm{d}x} =$ |
$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(1-\cos\left(x\right){\cdot}\sin\left(x\right)\right)}}$ $=\class{steps-node}{\cssId{steps-node-2}{-\class{steps-node}{\cssId{steps-node-3}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\cos\left(x\right){\cdot}\sin\left(x\right)\right)}}}}$ $=-\left(\class{steps-node}{\cssId{steps-node-5}{\class{steps-node}{\cssId{steps-node-4}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\cos\left(x\right)\right)}}{\cdot}\sin\left(x\right)}}+\class{steps-node}{\cssId{steps-node-7}{\cos\left(x\right){\cdot}\class{steps-node}{\cssId{steps-node-6}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\sin\left(x\right)\right)}}}}\right)$ $=-\class{steps-node}{\cssId{steps-node-8}{\left(-\sin\left(x\right)\right)}}{\cdot}\sin\left(x\right)-\class{steps-node}{\cssId{steps-node-9}{\cos\left(x\right)}}{\cdot}\cos\left(x\right)$ $={\left(\sin\left(x\right)\right)}^{2}-{\left(\cos\left(x\right)\right)}^{2}$ |
