Question

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

Derivatives
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asked 2021-05-23
Find derivatives for the functions. Assume a, b, c, and k are constants.
\(\displaystyle\omega{\left({r}\right)}=\sqrt{{{r}^{{{4}}}+{1}}}\)

Answers (1)

2021-05-24
\(\displaystyle\omega{\left({r}\right)}={\left(\sqrt{{{r}^{{{4}}}+{1}}}\right)}'\)
\(\displaystyle={\frac{{{\left({r}^{{{4}}}+{1}\right)}}}{'}}\rbrace{\left\lbrace{2}\sqrt{{{r}^{{{4}}}+{1}}}\right\rbrace}\)
\(\displaystyle={\frac{{{4}{r}^{{{3}}}}}{{{2}\sqrt{{{r}^{{{4}}}+{1}}}}}}\)
\(\displaystyle={\frac{{{2}{r}^{{{2}}}}}{{\sqrt{{{r}^{{{4}}}+{1}}}}}}\)
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