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Pochodna funkcji sqrt(sin(3x))

$f\left(x\right) =$	$\sqrt{\sin\left(3x\right)}$
$\dfrac{\mathrm{d}\left(f\left(x\right)\right)}{\mathrm{d}x} =$	$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\sqrt{\sin\left(3x\right)}\right)}}$ $=\class{steps-node}{\cssId{steps-node-2}{\dfrac{1}{2{\cdot}\sqrt{\sin\left(3x\right)}}}}{\cdot}\class{steps-node}{\cssId{steps-node-3}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\sin\left(3x\right)\right)}}$ $=\dfrac{\class{steps-node}{\cssId{steps-node-4}{\cos\left(3x\right)}}{\cdot}\class{steps-node}{\cssId{steps-node-5}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(3x\right)}}}{2{\cdot}\sqrt{\sin\left(3x\right)}}$ $=\dfrac{\class{steps-node}{\cssId{steps-node-6}{3}}{\cdot}\cos\left(3x\right)}{2{\cdot}\sqrt{\sin\left(3x\right)}}$

$f\left(x\right) =$

$\sqrt{\sin\left(3x\right)}$

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

$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\sqrt{\sin\left(3x\right)}\right)}}$

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

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

$=\dfrac{\class{steps-node}{\cssId{steps-node-6}{3}}{\cdot}\cos\left(3x\right)}{2{\cdot}\sqrt{\sin\left(3x\right)}}$