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Pochodna funkcji arcsinx+arcsinsqrt1-x^2

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

$f\left(x\right) =$

$\arcsin\left(x\right)-{x}^{2}+\dfrac{{\pi}}{2}$

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

$\class{steps-node}{\cssId{steps-node-1}{\tfrac{\mathrm{d}}{\mathrm{d}x}\kern-.25em\left(\arcsin\left(x\right)-{x}^{2}+\dfrac{{\pi}}{2}\right)}}$

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

$=\class{steps-node}{\cssId{steps-node-5}{\dfrac{1}{\sqrt{1-{x}^{2}}}}}-\class{steps-node}{\cssId{steps-node-6}{2}}\class{steps-node}{\cssId{steps-node-7}{x}}$