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Pochodna funkcji (e^(2x)/(-3))(sin(x)+2cos(x))

$f\left(x\right) =$	$\dfrac{-{\mathrm{e}}^{2x}{\cdot}\left(\sin\left(x\right)+2{\cdot}\cos\left(x\right)\right)}{3}$ Note: Your input has been rewritten/simplified.
$\dfrac{\mathrm{d}\left(f\left(x\right)\right)}{\mathrm{d}x} =$	$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\dfrac{-{\mathrm{e}}^{2x}{\cdot}\left(\sin\left(x\right)+2{\cdot}\cos\left(x\right)\right)}{3}\right)}}$ $=\class{steps-node}{\cssId{steps-node-2}{\dfrac{-\class{steps-node}{\cssId{steps-node-3}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({\mathrm{e}}^{2x}{\cdot}\left(\sin\left(x\right)+2{\cdot}\cos\left(x\right)\right)\right)}}}{3}}}$ $=\dfrac{-\left(\class{steps-node}{\cssId{steps-node-5}{\class{steps-node}{\cssId{steps-node-4}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({\mathrm{e}}^{2x}\right)}}{\cdot}\left(\sin\left(x\right)+2{\cdot}\cos\left(x\right)\right)}}+\class{steps-node}{\cssId{steps-node-7}{{\mathrm{e}}^{2x}{\cdot}\class{steps-node}{\cssId{steps-node-6}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\sin\left(x\right)+2{\cdot}\cos\left(x\right)\right)}}}}\right)}{3}$ $=\dfrac{-\left(\class{steps-node}{\cssId{steps-node-8}{{\mathrm{e}}^{2x}}}{\cdot}\class{steps-node}{\cssId{steps-node-9}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(2x\right)}}\right){\cdot}\left(\sin\left(x\right)+2{\cdot}\cos\left(x\right)\right)-\class{steps-node}{\cssId{steps-node-10}{\left(\class{steps-node}{\cssId{steps-node-11}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\sin\left(x\right)\right)}}+2{\cdot}\class{steps-node}{\cssId{steps-node-12}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\cos\left(x\right)\right)}}\right)}}{\cdot}{\mathrm{e}}^{2x}}{3}$ $=\dfrac{-\class{steps-node}{\cssId{steps-node-13}{2}}{\mathrm{e}}^{2x}{\cdot}\left(\sin\left(x\right)+2{\cdot}\cos\left(x\right)\right)-\left(2{\cdot}\class{steps-node}{\cssId{steps-node-15}{\left(-\sin\left(x\right)\right)}}+\class{steps-node}{\cssId{steps-node-14}{\cos\left(x\right)}}\right){\cdot}{\mathrm{e}}^{2x}}{3}$ $=\dfrac{-2{\mathrm{e}}^{2x}{\cdot}\left(\sin\left(x\right)+2{\cdot}\cos\left(x\right)\right)-{\mathrm{e}}^{2x}{\cdot}\left(\cos\left(x\right)-2{\cdot}\sin\left(x\right)\right)}{3}$ Wynik alternatywny: $=\dfrac{-2{\mathrm{e}}^{2x}{\cdot}\left(\sin\left(x\right)+2{\cdot}\cos\left(x\right)\right)}{3}-\dfrac{{\mathrm{e}}^{2x}{\cdot}\left(\cos\left(x\right)-2{\cdot}\sin\left(x\right)\right)}{3}$

$f\left(x\right) =$

$\dfrac{-{\mathrm{e}}^{2x}{\cdot}\left(\sin\left(x\right)+2{\cdot}\cos\left(x\right)\right)}{3}$

Note: Your input has been rewritten/simplified.

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

$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\dfrac{-{\mathrm{e}}^{2x}{\cdot}\left(\sin\left(x\right)+2{\cdot}\cos\left(x\right)\right)}{3}\right)}}$

$=\class{steps-node}{\cssId{steps-node-2}{\dfrac{-\class{steps-node}{\cssId{steps-node-3}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({\mathrm{e}}^{2x}{\cdot}\left(\sin\left(x\right)+2{\cdot}\cos\left(x\right)\right)\right)}}}{3}}}$

$=\dfrac{-\left(\class{steps-node}{\cssId{steps-node-5}{\class{steps-node}{\cssId{steps-node-4}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left({\mathrm{e}}^{2x}\right)}}{\cdot}\left(\sin\left(x\right)+2{\cdot}\cos\left(x\right)\right)}}+\class{steps-node}{\cssId{steps-node-7}{{\mathrm{e}}^{2x}{\cdot}\class{steps-node}{\cssId{steps-node-6}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\sin\left(x\right)+2{\cdot}\cos\left(x\right)\right)}}}}\right)}{3}$

$=\dfrac{-\left(\class{steps-node}{\cssId{steps-node-8}{{\mathrm{e}}^{2x}}}{\cdot}\class{steps-node}{\cssId{steps-node-9}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(2x\right)}}\right){\cdot}\left(\sin\left(x\right)+2{\cdot}\cos\left(x\right)\right)-\class{steps-node}{\cssId{steps-node-10}{\left(\class{steps-node}{\cssId{steps-node-11}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\sin\left(x\right)\right)}}+2{\cdot}\class{steps-node}{\cssId{steps-node-12}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\cos\left(x\right)\right)}}\right)}}{\cdot}{\mathrm{e}}^{2x}}{3}$

$=\dfrac{-\class{steps-node}{\cssId{steps-node-13}{2}}{\mathrm{e}}^{2x}{\cdot}\left(\sin\left(x\right)+2{\cdot}\cos\left(x\right)\right)-\left(2{\cdot}\class{steps-node}{\cssId{steps-node-15}{\left(-\sin\left(x\right)\right)}}+\class{steps-node}{\cssId{steps-node-14}{\cos\left(x\right)}}\right){\cdot}{\mathrm{e}}^{2x}}{3}$

$=\dfrac{-2{\mathrm{e}}^{2x}{\cdot}\left(\sin\left(x\right)+2{\cdot}\cos\left(x\right)\right)-{\mathrm{e}}^{2x}{\cdot}\left(\cos\left(x\right)-2{\cdot}\sin\left(x\right)\right)}{3}$

Wynik alternatywny:

$=\dfrac{-2{\mathrm{e}}^{2x}{\cdot}\left(\sin\left(x\right)+2{\cdot}\cos\left(x\right)\right)}{3}-\dfrac{{\mathrm{e}}^{2x}{\cdot}\left(\cos\left(x\right)-2{\cdot}\sin\left(x\right)\right)}{3}$