Pregunta: derivada por lagaritmos y=x-1x4+12

Use $\sqrt[\mathrm{n}]{{\mathrm{a}}^{\mathrm{x}}}={\mathrm{a}}^{\frac{\mathrm{x}}{\mathrm{n}}}$ to rewrite $\sqrt{\frac{\mathrm{x}-1}{{\mathrm{x}}^4+1}}$ as ${\left(\frac{\mathrm{x}-1}{{\mathrm{x}}^4+1}\right)}^{\frac{1}{2}}$ .

$\frac{\mathrm{d}}{\mathrm{d}\mathrm{x}}\left[{\left(\frac{\mathrm{x}-1}{{\mathrm{x}}^4+1}\right)}^{\frac{1}{2}}\right]$

Differentiate using the chain rule, which states that $\frac{\mathrm{d}}{\mathrm{d}\mathrm{x}}\left[\mathrm{f}\left(\mathrm{g}\left(\mathrm{x}\right)\right)\right]$ is ${\mathrm{f}}^{\prime }\left(\mathrm{g}\left(\mathrm{x}\right)\right){\mathrm{g}}^{\prime }\left(\mathrm{x}\right)$ where $\mathrm{f}\left(\mathrm{x}\right)={\mathrm{x}}^{\frac{1}{2}}$ and $\mathrm{g}\left(\mathrm{x}\right)=\frac{\mathrm{x}-1}{{\mathrm{x}}^4+1}$ .