# Find derivatives for the functions. Assume a, b, c, and k are constants. \omega (r)=\sqrt{r^{4}+1}

Derivatives
Find derivatives for the functions. Assume a, b, c, and k are constants.
$$\displaystyle\omega{\left({r}\right)}=\sqrt{{{r}^{{{4}}}+{1}}}$$

$$\displaystyle\omega{\left({r}\right)}={\left(\sqrt{{{r}^{{{4}}}+{1}}}\right)}'$$
$$\displaystyle={\frac{{{\left({r}^{{{4}}}+{1}\right)}}}{'}}\rbrace{\left\lbrace{2}\sqrt{{{r}^{{{4}}}+{1}}}\right\rbrace}$$
$$\displaystyle={\frac{{{4}{r}^{{{3}}}}}{{{2}\sqrt{{{r}^{{{4}}}+{1}}}}}}$$
$$\displaystyle={\frac{{{2}{r}^{{{2}}}}}{{\sqrt{{{r}^{{{4}}}+{1}}}}}}$$