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

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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casincal
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 $$\displaystyle{\frac{{{d}}}{{{d}{u}}}}{\left({u}^{{{n}}}\right)}=\nu^{{{n}-{1}}}$$
$$\displaystyle={8}{\left({\frac{{{3}}}{{{4}}}}\right)}{u}^{{{\frac{{{3}}}{{{4}}}}-{1}}}+{4}{\left(-{\frac{{{1}}}{{{4}}}}\right)}{u}^{{{\frac{{-{1}}}{{{u}}}}-{1}}}$$
$$\displaystyle={6}{u}^{{{\frac{{-{1}}}{{{u}}}}}}-{u}^{{{\frac{{-{5}}}{{{4}}}}}}$$
$$\displaystyle={\frac{{{6}}}{{{u}^{{{\frac{{{1}}}{{{4}}}}}}}}}-{\frac{{{1}}}{{{u}^{{{\frac{{{5}}}{{{4}}}}}}}}}$$