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Pochodna funkcji arcsin(sqrt(x))

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

$f\left(x\right) =$

$\arcsin\left(\sqrt{x}\right)$

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

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

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

$=\dfrac{\class{steps-node}{\cssId{steps-node-4}{\dfrac{1}{2{\cdot}\sqrt{x}}}}}{\sqrt{1-x}}$

$=\dfrac{1}{2{\cdot}\sqrt{1-x}{\cdot}\sqrt{x}}$