Question

Compute the following derivatives \frac{d}{ds}[(s^{3}-7s)^{\frac{8}{3}}]

Derivatives
ANSWERED
asked 2021-05-02
Compute the following derivatives
\(\displaystyle{\frac{{{d}}}{{{d}{s}}}}{\left[{\left({s}^{{{3}}}-{7}{s}\right)}^{{{\frac{{{8}}}{{{3}}}}}}\right]}\)

Answers (1)

2021-05-03
\(\displaystyle{y}={\left({s}^{{{3}}}-{7}{s}\right)}^{{\frac{{8}}{{3}}}}\)
Differentiating with respect to s
\(\displaystyle{y}'={\left(\frac{{8}}{{3}}\right)}{\left({s}^{{{3}}}-{7}{s}\right)}^{{{\left(\frac{{8}}{{3}}\right)}-{1}}}\times{\left({3}{s}^{{{2}}}-{7}\right)}\)
\(\displaystyle{y}'={\left(\frac{{8}}{{3}}\right)}{\left({3}{s}^{{{2}}}-{7}\right)}{\left({s}^{{{3}}}-{7}{s}\right)}^{{\frac{{5}}{{3}}}}\)
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