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