Find the indicated derivatives. \frac{d}{du}(8u^{\frac{3}{4}}+4u

Tobias Ali 2021-10-01 Answered
Find the indicated derivatives.
\(\displaystyle{\frac{{{d}}}{{{d}{u}}}}{\left({8}{u}^{{{\frac{{{3}}}{{{4}}}}}}+{4}{u}^{{-{\frac{{{1}}}{{{4}}}}}}\right)}\)

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Expert Answer

casincal
Answered 2021-10-02 Author has 9744 answers
Step 1
Given:
\(\displaystyle{\frac{{{d}}}{{{d}{u}}}}{\left({8}{u}^{{{\frac{{{3}}}{{{4}}}}}}+{4}{u}^{{-{\frac{{{1}}}{{{4}}}}}}\right)}\)
Step 2
\(\displaystyle={8}{\frac{{{d}}}{{{d}{u}}}}{\left({u}^{{{\frac{{{3}}}{{{4}}}}}}\right)}+{4}{\frac{{{d}}}{{{d}{u}}}}{\left({u}^{{-{\frac{{{1}}}{{{4}}}}}}\right)}\)
using \(\displaystyle{\frac{{{d}}}{{{d}{u}}}}{\left({u}^{{{n}}}\right)}=\nu^{{{n}-{1}}}\)
\(\displaystyle={8}{\left({\frac{{{3}}}{{{4}}}}\right)}{u}^{{{\frac{{{3}}}{{{4}}}}-{1}}}+{4}{\left(-{\frac{{{1}}}{{{4}}}}\right)}{u}^{{{\frac{{-{1}}}{{{u}}}}-{1}}}\)
\(\displaystyle={6}{u}^{{{\frac{{-{1}}}{{{u}}}}}}-{u}^{{{\frac{{-{5}}}{{{4}}}}}}\)
\(\displaystyle={\frac{{{6}}}{{{u}^{{{\frac{{{1}}}{{{4}}}}}}}}}-{\frac{{{1}}}{{{u}^{{{\frac{{{5}}}{{{4}}}}}}}}}\)
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