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Pochodna funkcji xarcsinx

$f\left(x\right) =$	$x{\cdot}\arcsin\left(x\right)$
$\dfrac{\mathrm{d}\left(f\left(x\right)\right)}{\mathrm{d}x} =$	$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(x{\cdot}\arcsin\left(x\right)\right)}}$ $=\class{steps-node}{\cssId{steps-node-3}{\class{steps-node}{\cssId{steps-node-2}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(x\right)}}{\cdot}\arcsin\left(x\right)}}+\class{steps-node}{\cssId{steps-node-5}{x{\cdot}\class{steps-node}{\cssId{steps-node-4}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\arcsin\left(x\right)\right)}}}}$ $=\class{steps-node}{\cssId{steps-node-6}{1}}{\cdot}\arcsin\left(x\right)+\class{steps-node}{\cssId{steps-node-7}{\dfrac{1}{\sqrt{1-{x}^{2}}}}}{\cdot}x$ $=\arcsin\left(x\right)+\dfrac{x}{\sqrt{1-{x}^{2}}}$

$f\left(x\right) =$

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

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

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

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

$=\class{steps-node}{\cssId{steps-node-6}{1}}{\cdot}\arcsin\left(x\right)+\class{steps-node}{\cssId{steps-node-7}{\dfrac{1}{\sqrt{1-{x}^{2}}}}}{\cdot}x$

$=\arcsin\left(x\right)+\dfrac{x}{\sqrt{1-{x}^{2}}}$